International Journal of Mathematical Modelling and Numerical Optimisation (26 papers in press)

Regular Issues

• Multi-modal emotion recognition from speech, facial expression, video and text modalities: a review  
  by Ruchi Chauhan, Nirmala Sharma, Ajay Sharma 
  Abstract: Multi-modal emotion recognition, which leverages the combined strengths of speech, facial expressions, video, and textual information, has become a cornerstone in the development of emotionally intelligent technologies. By capturing the complexity of human emotions more accurately than single-modality systems, multi-modal approaches offer transformative benefits across various sectors of society. In mental health, they enable early detection of emotional distress and support remote psychological monitoring. In education, emotion-aware systems foster adaptive learning environments tailored to students' emotional states. Public safety applications benefit from improved behavioral analysis, while customer service is enhanced through more empathetic and personalized interactions. This review presents a comprehensive overview of recent progress in emotion recognition from each modality over the past decade, focusing on innovative methods for extracting, combining, and interpreting emotional signals.
  Keywords: multi-modal emotion recognition; MER; speech emotion recognition; facial emotion recognition; video emotion recognition; text emotion recognition; machine-human interaction.
  DOI: 10.1504/IJMMNO.2026.10073643
   
  
• Modelling, optimisation, and experimental evaluation of predictive maintenance strategies for LiFePO₄ battery health in e-bikes  
  by Appalabathula Venkatesh, Simhadri Phani Kumar, Tousif Khan Nizami 
  Abstract: The rapid expansion of the electric vehicle (EV) sector has heightened the need for advanced battery management systems (BMS) to ensure lithium-based batteries safety, reliability, and efficiency. This study presents the design and real-time implementation of a 72 V, 36A h LiFePO₄ e-bike battery pack integrated with an active balancing BMS. This research study uniquely combines the real-world GPS-tracked e-bike testbed, evaluated for range testing, and data were collected across varying terrains, speeds, and riding conditions. BMS data voltage, current, temperature, and health indicators are analysed to identify operational trends, deviations from ideal performance, and early signs of battery degradation. The designed e-bikes theoretical range was estimated at 67 km, while practical testing demonstrated an extended range of 70.15 km, reflecting a 4.7% improvement. Simulation outcomes were validated against experimental outcomes, yielding deviations of 0.02 and 0.5 V in buck and boost output voltages, 0.015 and 0.333 A in currents, and a SoC deviation of 0.6%. These results confirm the effectiveness of the designed e-bike modelling in electric vehicle applications.
  Keywords: electric vehicles; case study; battery management system; electric bike; converter; experimental validation.
  DOI: 10.1504/IJMMNO.2026.10073645
   
  
• Aggregation and Segmentation for Optimising Load-Bearing Structures  
  by Michael Todinov 
  Abstract: The paper presents a very powerful method in structural engineering, referred to as the method of aggregation, for reducing the weight and increasing load capacity of structures. Rigorous results have been stated and proved, forming the foundation of the aggregation method for structures composed of beams with arbitrarily shaped cross-sections. The essence of this method, overlooked in modern stress analysis, lies in consolidating loaded elements into a reduced number of elements with larger cross-sections, thereby significantly decreasing the material required to support a given total load. For cantilever and simply supported beams, the reduction in material volume, deflection, and stress depends only on the scaling factor of the cross-section along the y-axis and is independent of the scaling factor along the x-axis. The aggregation method was tested by a case study and finite element experiments involving structures built on statically determinate cantilever beams. These studies confirmed that aggregating elements loaded in bending leads to a drastic increase of the load capacity of the structures and a drastic decrease of both the maximum von Mises stress and the maximum deflection.
  Keywords: light-weight design; load capacity; aggregation; segmentation; structural optimisation; cantilever beams; simply loaded beams; bending.
  DOI: 10.1504/IJMMNO.2026.10074638
   
  
• Semi-recursive estimation of multidimensional regression function using the generalised Bernstein polynomial  
  by D.A.N. Njamen, M.A. Issaka, B. Baldagai 
  Abstract: The aim of this article is to use the stochastic approximation method and the generalised Bernstein polynomial to construct an extension of the semi-recursive estimator for the multivariate regression function. We investigate some asymptotic properties of the proposed estimator and determine the optimal parameters that minimise the mean squared error using a cross-validation procedure. Finally, numerical simulation studies show that for these optimal parameters, the proposed estimator has better properties near the edges than kernel-type estimators when the support of the function to be estimated is bounded on at least one side. A real-world application of the proposed estimator on the COVID-19 epidemic in a Chadian hospital showed that the proposed model and the Nadaraya-Watson estimator appear more robust than the kernel-type estimator.
  Keywords: stochastic approximation methods; multivariate regression; Bernstein polynomial; asymptotic properties; cross-validation method; semi-recursivity.
  DOI: 10.1504/IJMMNO.2026.10075411
   
  
• Modelling social media virality with deep learning: insights from Bhopal, India  
  by H.A. Bhavithra, Jebamalar Tamilselvi Jeyaraj, V. Uma Rani, S. Sindu Devi 
  Abstract: Social media platforms, such as WeChat, are central to communication, information sharing, and opinion formation. Understanding how information spreads is vital for combating misinformation, optimising marketing, and enhancing engagement. This study adapts the susceptible-forward-removed (SFR) model, where susceptible users may read messages, forward users share them, and removed users ignore or have already engaged. Mirroring disease transmission, diffusion dynamics are shaped by network structures. Key metrics, including stability thresholds and spread ratios, are analysed alongside sensitivity tests for misinformation control. Numerical simulations via the Runge-Kutta method produce consistent patterns. A recurrent neural network (RNN) is integrated to capture temporal dependencies in SFR counts. Experimental results show RNN outperforms other machine and deep learning models, achieving the lowest MAE (0.020074) and RMSE (0.031919). Accurate SFR prediction provides critical insights into diffusion processes and supports strategic interventions in online communities.
  Keywords: information stability threshold; information spread ratio; sensitivity analysis; Runge-Kutta method; recurrent neural network; RNN; India.
  DOI: 10.1504/IJMMNO.2027.10075551
   
  
• Solving a linear programming problem with greater than equal to constraints using resultant vector ascent method  
  by Subhadip Sarkar 
  Abstract: An iterative method is proposed for minimising a linear programming problem containing all surplus variables, which facilitates the movement from an interior point to the facets through the path traced within the interior of the feasible space while incorporating a resultant vector ascent method and a cutting plane. This approach does not suffer from the looping problem during degeneracy. The proposed vectors, located in the null space of the transformed technological matrix, aid in minimising the problem within the t number (≤m < n) of steps where n and m represent the number of variables and constraints (including the cutting plane). The concepts of elementary column operation and highest cost contribution are administered here to select the appropriate vector in each iteration. This model brings the optimal solution with a worst-case time complexity of O(nm(n m)) which seems faster than the Big-M method, even at n = 2m amidst all positive model coefficients.
  Keywords: linear programming; Big-M Method; resultant vector ascent method.
  DOI: 10.1504/IJMMNO.2026.10075553
   
  
• A modification of weak disposability in non-parametric analysis  
  by Mahnaz Maghbouli, Azam Pourhabib Yekta, Josef Jablonsky 
  Abstract: Data envelopment analysis (DEA) studies in environmental assessment have relied on the comprehensive economic concept of weak disposability as a framework. Dealing with undesirable results in the last decade has often involved using the weak disposability axiom instead of sticking to the idea of free disposability. Having used the axiom of weak disposability enables more accurate efficiency measurement of decision making units (DMUs) while reduces the detrimental effects of undesirable outputs on environment. To effectively tackle with undesirable outputs, this study presents a non-radial model grounded in original technology. By incorporating an abatement factor, this study's key contribution is to redefine a model that accurately measures the reduction of undesirable outputs. Empirical instances reveal the superiority of the proposed model, showcasing its usefulness and enhanced performance compared to its counterpart.
  Keywords: data envelopment analysis; DEA; decision making units; DMUs; abatement factor; undesirable outputs; weak disposability; environmental performance.
  DOI: 10.1504/IJMMNO.2027.10075991
   
  
• Laplace HPM in Caputo and Caputo Fabrizio sense regarding semi analytical solution of fractional-order system of Drinfeld-Sokolov-Wilson equation  
  by Mamta Kapoor 
  Abstract: This paper proposes two innovative semi-analytical solution methods for the fractional Drinfeld-Sokolov-Wilson (DSW) equations, aiming to more efficiently address complex systems characterized by memory effects and anomalous diffusion. This model has several applications in fluid mechanics, plasma physics, and integrable systems. The fractional formulation DSW equation contains essential memory effects and anomalous transport phenomena, which are rarely described by classical integer-order models. To address computational aspects of fractional systems, two novel semi-analytical approaches are proposed: Method I is Laplace transform coupled with the homotopy perturbation method under Caputo derivative and Method II contains same framework under Caputo-Fabrizio derivative. Such methods are selected for their ability to handle fractional operators efficiently without any need of grid discretization. Key results demonstrate that these methods achieve a good compatibility with exact solutions, which is validated through absolute error analysis. Notably, Caputo-based approach consistently outperforms its Caputo-Fabrizio based results (most of the times) in accuracy.
  Keywords: Laplace HPM; Caputo fractional derivative; Caputo Fabrizio fractional derivative; fractional Drinfeld-Sokolov-Wilson equation.
  DOI: 10.1504/IJMMNO.2027.10076094
   
  
• Study of heat conduction process inside the nip of soft calender used in electrode production for Li-ion batteries  
  by Sonali Rangra, Neel Kanth, Jitendra Kumar 
  Abstract: Due to an exponential growing demand of Li-ion batteries, the requirement to enhance and improve the overall performance of the battery is also growing. In an electrode production process, the final step is the calendering process, which greatly impact the overall performance of the Li-ion batteries. Temperature of the bowl, contact time, and nip pressure are the basic parameters of a calendering process, which lead to a change in the mechanical, microstructural, and electrochemical properties of an electrode sheet. This paper aims to determine the effect of basic parameters on the temperature of electrode sheet in the stiffness/thickness direction by utilising Heat Conduction model when a sheet of electrode is passed through the calender nip formed by two bowls having same and different profiles of temperature. The variational iteration method is adopted to approximate the developed model, which evidently depicts the performance and behaviour of the model.
  Keywords: variational iteration method; lithium-ion batteries; electrode production; calendering process; contact time; nip width; thermal diffusivity; porosity; energy density; electric vehicles.
  DOI: 10.1504/IJMMNO.2027.10078056
   
  
• Two methods for finding invariant solutions of Guéant-Pu option pricing model with Riemann-Liouville derivative  
  by Khristofor V. Yadrikhinskiy, Vladimir E. Fedorov 
  Abstract: We study the fractional Guéant-Pu equation, which models option pricing taking into account transaction costs and the long-term impact of operations on the market. Based on the previously obtained group classification of the equation, optimal systems of one-dimensional and two-dimensional subalgebras of Lie algebras are calculated. For these subalgebras, six invariant submodels are derived. They are combined into two triples of submodels. Every triple is considered in the framework of one general submodel. For the first general submodel, invariant solutions are obtained by the Lie-Ovsyannikov method. To the second general submodel a number of invariant solutions is found using the invariant subspace method. These results obtained in two different ways lead to obtaining a series of exact solutions to the model under study.
  Keywords: Riemann-Liouville fractional derivative; group analysis; Lie algebra; optimal system of subalgebras; invariant submodel; invariant solution; Lie-Ovsyannikov method; invariant subspace method.
  DOI: 10.1504/IJMMNO.2027.10076426
   
  
• Modelling-oriented robust fault-tolerant control design for multi-agent systems with bounded disturbances and actuator degradation: an LMI-based stability analysis  
  by T. Poongodi, T. Thiyagarajan 
  Abstract: In this work, new results on robust fault-tolerant control design for multi-agent systems with bounded disturbances and actuator failures is investigated. Particularly, a new control model is implemented in which actuator fault matrix obeys a certain sufficient criteria. Based on the proper Lyapunov-Krasovskii functional and integral inequality approach, a novel sufficient criteria is constructed in the form of linear matrix inequalities. Under obtained linear matrix inequalities, the closed-loop system is asymptotically stable. Finally, a numerical example is given to validate the effectiveness of the considered method.
  Keywords: multi-agent systems; fault-tolerant control; bounded disturbances; linear matrix inequalities.
  DOI: 10.1504/IJMMNO.2027.10076599
   
  
• Analysis of a two phase Mx/G/1 retrial G-queue with starting failure and search of customers in optical burst switching network  
  by S.T. Sowmya Narayani, D. Sumitha  
  Abstract: We discuss a single server retrial G-queue with search of customers in Optical Burst Switching Network. The server may fail when attempting to start. The server operates two distinct service phases; essential and M-multi-optional service. There are two types of incoming customers Positive customers arrive in batches. If the server is unoccupied and starts the service successfully then one of them get the service immediately while others enter the orbit. After completing each phase of service, if the customer departs the system, the server searches for the customers in the orbit. When a negative customer arrives, it causes the server to crash, which forces the interrupted customer to leave and the repair for the server begins immediately. Using the supplementary variable technique, performance measures are obtained. Reliability indices, expected busy period and cycle are derived. Influences of the different parameters are analysed numerically and cost optimisation is presented.
  Keywords: positive customer; negative customer; starting failure; orbital search; m-multi-optional services.
  DOI: 10.1504/IJMMNO.2027.10076600
   
  
• Optimising electric vehicle energy management strategy using deep reinforcement learning and linear regression models  
  by Sudheer Hanumanthakari, Ramanjaneya Reddy Nalavala, Badugu Suresh, Madhavilatha Idimadakala, Venkatesh Peruthambi 
  Abstract: Intelligent energy management is vital for electric vehicles (EVs) to enhance performance, extend driving range, and minimise energy consumption. Conventional approaches such as linear regression (LR) and other machine learning models have been used for power prediction and allocation; however, they exhibit limited adaptability under nonlinear and dynamic driving conditions. Deep reinforcement learning (DRL) provides adaptive optimisation but faces challenges related to computational complexity and training instability with incomplete or noisy data. To address these limitations, this paper proposes a hybrid linear regression-deep reinforcement learning (LR-DRL) framework for real-time energy management in EVs. In this framework, LR generates baseline energy forecasts that guide the DRL agent to refine real-time power allocation and optimise regenerative braking performance. Simulation outcomes reveal that the proposed LR-DRL approach achieves up to a 25% improvement in energy efficiency, ensuring enhanced adaptability, robustness, and sustainability compared to existing energy management strategies.
  Keywords: deep reinforcement learning; DRL; energy management; electric vehicles; linear regression; predictive modelling.
  DOI: 10.1504/IJMMNO.2027.10076798
   
  
• Semi-analytical solutions of conformable fractional Cauchy reaction-diffusion equations using Shehu Adomian decomposition method  
  by Mamta Kapoor 
  Abstract: The goal of this study is to use the Shehu Adomian decomposition method to obtain the semi-analytical solutions of the conformable fractional Cauchy reaction-diffusion equations. The suggested method is created by combining the Adomian decomposition method with the Shehu transform. Additionally, the approximated and exact solutions’ graphical compatibility is offered. Additionally, the concept of the L∞ error norm is used to test the numerical convergence. The suggested regime’s theoretical convergence and uniqueness are also examined. Over a broad range of time levels, good compatibility between approximated and exact solutions is achieved. Since there are no discretisation, linearisation, or quasi-linearisation errors, the current method is a good substitute for numerical methods. The proposed method provides a powerful alternative to traditional numerical methods by removing the discretisation, linearisation, and quasi-linearisation flaws. Because of its precision and adaptability, it is perfect for modelling real-world events in fields like biology, engineering, and physics.
  Keywords: Shehu transform; Adomian decomposition method; ADM; graphical plots.
  DOI: 10.1504/IJMMNO.2027.10076896
   
  
• A sustainable inventory model with advance payment, learning curve and performance-based carbon refunds  
  by Lisa Bora, Nabendu Sen 
  Abstract: This study develops a sustainable single-product inventory model that integrates advance customer payments, green investment, a learning-curve-based production cost, and a performance-based carbon refund. Inventory dynamics are formulated through differential equations, linking the financial mechanism of advance payments to environmentally driven decisions: a fixed share of the advance is invested in emission-reduction measures, with a partial refund granted if emissions remain below a regulatory cap. The nonlinear profit-maximisation problem is solved using two metaheuristic algorithms weighted particle swarm optimisation (WPSO) and constriction factor PSO (CPSO) which converge to the same global optimum. Numerical results indicate that allocating 89.90% of the advance to sustainability triggers the refund, achieves a 6940.21% return on green investment, and increases profit by 660% compared to the no-investment scenario. These findings demonstrate how strategic coupling of financial design and operational planning can simultaneously enhance profitability and meet environmental objectives.
  Keywords: sustainable inventory model; advance payment; green investment; carbon refund; PSO optimisation; learning curve.
  DOI: 10.1504/IJMMNO.2027.10077132
   
  
• An efficient load balancing strategy using modified grey wolf optimiser for cloud computing  
  by Priyanka Meiwal, Nirmala Sharma 
  Abstract: Load balancing aims to ensure that all VMs share an equal and fair load, which in turn enhances resource utilisation and overall system performance. This article introduces an efficient load-balancing strategy utilising the grey wolf optimiser (GWO) algorithm within a cloud environment. The proposed technique is termed as load balancing using modified grey wolf optimiser (LBMGWO) algorithm. This method effectively schedules tasks and balances the load across VMs in the data centre. The implementation of the proposed LBMGWO strategy is carried out using Apache NetBeans IDE, and the performance is evaluated based on two metrics namely, the makespan and resource usage. The experiments are carried out for three to five virtual machines with task ranging from 10 to 50. The obtained results indicate that the LBMGWO algorithm outperforms in comparison with other state-of-the-art algorithms in the literature by effectively minimising the makespan and maximising resource usage.
  Keywords: load balancing; cloud computing; swarm-intelligence; grey wolf optimiser; GWO; makespan.
  DOI: 10.1504/IJMMNO.2027.10077474
   
  
• Solution of a fractional order model for lumpy skin disease by adomian decomposition general transform method  
  by Bijal Yeolekar, Dhiren Pandit, Anup Singh, Radhika Dave 
  Abstract: Lumpy skin disease (LSD) is a viral infection in cattle, predominantly transmitted by vectors, and is associated with significant economic losses in the livestock industry. This study proposes a fractional-order mathematical model that incorporates memory effects and nonlocal interactions. The cattle population is stratified into susceptible, exposed, infectious, and recovered compartments, explicitly considering the role of both infected and susceptible vectors in disease transmission. Stability analysis of the equilibrium points is performed to determine the conditions under which the disease persisted or died out, and the sensitivity analysis is carried out. Bifurcation analysis is conducted to highlight the critical thresholds that can lead to disease outbreaks or eradication. Numerical simulations have confirmed that the fractional-order framework offers richer and more realistic insights into LSD dynamics than integer-order models. Overall, these findings emphasise the powerful approach for designing effective control measures and improving predictive accuracy in LSD management.
  Keywords: lumpy skin disease; LSD; fractional-order model; Caputo derivative; vector-borne transmission; SEIR model; stability analysis; numerical simulation; disease dynamics; memory effects.
  DOI: 10.1504/IJMMNO.2027.10077475
   
  
• Mathematical modelling of adaptive fisheries management using reinforcement learning  
  by I. Ait El Harch , Khalid Outaaoui, Y. El Foutayeni 
  Abstract: This study explores the integration of bioeconomic modelling and artificial intelligence to optimise fisheries management while promoting ecosystem sustainability. We first provide a general overview of bioeconomic models, highlighting previous research and the dual objectives of profit maximisation and ecological preservation. We then introduce a mathematical model representing the exploitation of a single species within a three species marine ecosystem. A detailed mathematical analysis is conducted to identify equilibrium points that ensure the persistence of all species, along with their positivity, boundedness, and stability. Building on this foundation, we apply reinforcement learning (RL) to the model, demonstrating how AI techniques can guide adaptive harvesting strategies. Finally, we perform a sensitivity analysis on key parameters influencing the RL implementation, providing insights into the robustness and effectiveness of the approach. Our findings highlight the potential of combining bioeconomic theory and AI to achieve sustainable resource management and inform future research directions.
  Keywords: mathematical modelling; bio-economical modelling; reinforcement learning; AI-based optimisation; optimisation techniques; fishery management.
  DOI: 10.1504/IJMMNO.2027.10077891
   
  
• Nonlinear bifurcation insights into measles control using fuzzy logic and dual-dose vaccination  
  by H.A. Bhavithra, S. Sindu Devi 
  Abstract: Measles remain to be a global health concern, particularly in resource-limited regions. This study develops a fuzzy epidemic model incorporating double-dose vaccination, time-varying transmission, and fuzzy parameterisation through a utility-based function to better represent uncertainty in disease dynamics. A fuzzy transmission threshold of approximately 0.0202 is identified, beyond which the fuzzy basic reproduction number exceeds unity, indicating potential outbreak conditions. Bifurcation analysis reveals transcritical, forward, and backward bifurcations, highlighting transitions between disease-free and endemic states and possible infection persistence. Numerical simulations using a Fibonacci polynomialbased collocation method validate theoretical results. The susceptible population decreases by 37.5%, single- and double-vaccinated populations by 22.1% and 30.7%, while exposed and infected populations drop by 15.7% and 39.8%. The recovered group initially rises by 19% then stabilises. The model effectively captures uncertainty and supports robust vaccination and control strategies under variable epidemiological conditions.
  Keywords: fuzzy mathematical model; fuzzy equilibrium points; stability analysis; transcritical bifurcation analysis; forward and backward bifurcation analysis.
  DOI: 10.1504/IJMMNO.2027.10077956
   
  
• Optimising the location of EV public charging stations in electrical distribution system using Giza Pyramid construction algorithm  
  by Sandip S. Yeole, Prakash G. Burade 
  Abstract: Electric vehicles (EVs) have substantial attention from the government and the industries due to lower carbon emissions, lower operating costs and reduced maintenance. However, as EV penetration increases, the load imposed by EVs impacts critical distribution network parameters, including power losses, voltage profiles, and harmonic distortion. To maintain the reliability of the distribution network, the strategic placement of public charging stations (PCSs) is essential. This paper proposes a two-stage methodology for determining optimal locations for PCSs. In the first stage, a public charging station operator index (PCSOI) is introduced, incorporating the land value index (LVI) and the EV population index (EVPI). The PCSOI is designed to minimise land value while maximising EV flow for the placement of PCSs. The formulated problem is solved using the Giza Pyramid Construction Algorithm (GPCA). Furthermore, GPCA demonstrated an average power loss reduction of 2.02% compared to the GWO method, highlighting its effectiveness.
  Keywords: Electric vehicle; public-charging stations; land value; Giza pyramid construction algorithm.
  DOI: 10.1504/IJMMNO.2027.10077957
   
  
• Analysis of curvature-controlled dynamics in Casson hybrid nanofluids with thermal slip and internal heat generation  
  by Veera Brahmam Yadavalli, R. Archanareddy, S. Sunitha Devi 
  Abstract: This study investigates the unsteady flow and heat transfer behaviour of temperature-dependent hybrid Casson nanofluids over curved geometries, considering thermal slip, velocity slip, viscous dissipation, and internal heat generation. The governing nonlinear partial differential equations for momentum and energy transport are solved numerically using a finite difference-based implicit scheme and validated against benchmark Newtonian and constant-property cases. The analysis highlights the influence of curvature on boundary layer development, showing that convex surfaces enhance heat transfer, while concave surfaces delay thermal response due to intensified recirculation. Incorporating hybrid Al₂O₃-Cu/water nanoparticles leads to a 22.4% increase in Nusselt number compared to mono-nanofluids, demonstrating the advantage of dual-particle dispersion. Temperature-dependent viscosity and thermal conductivity significantly modify wall shear stress and heat flux, while velocity and thermal slip reduce near-wall gradients. These findings provide actionable insights for engineering design, particularly in microchannel heat exchangers, biomedical cooling devices, and electronic systems. The study lays the groundwork for future exploration of turbulent flows, three-dimensional modelling, and AI-driven surrogate analysis of hybrid nanofluid systems.
  Keywords: Casson nanofluids; thermal slip; velocity slip; viscous dissipation; and internal heat generation; Nusselt number; and thermal energy systems.
  DOI: 10.1504/IJMMNO.2028.10078148
   
  
• A length-biased modified power Lindley distribution  
  by Suresha Kharvi  
  Abstract: Parametric models are often essential for analysing lifetime data, as they can accurately capture failure behaviour and hazard characteristics that nonparametric models may overlook. In this study, we introduce the length-biased modified power Lindley distribution to model data exhibiting inverted bathtub-shaped and increasing failure rates. We investigate the statistical properties of the proposed distribution and employ Descartes’ rule of signs to determine the possible shapes of its hazard rate function. The model parameters are estimated using the method of maximum likelihood, and a simulation study is conducted to evaluate the performance of these estimators. Furthermore, the stress-strength reliability parameter and its estimation are discussed. The practical utility of the proposed model is demonstrated by fitting it to two real-life datasets, where it provides a superior fit compared to several existing competing models.
  Keywords: length-biased modified power Lindley; maximum likelihood; Descartes’ algorithm; hazard rate function.
  DOI: 10.1504/IJMMNO.2027.10078221
   
  
• Analytical approach for solving the time-fractional Fornberg-Whitham equations via Sumudu transform  
  by R.K. Bairwa, Alka Santosh 
  Abstract: This article discusses approximate analytical solutions of the non-linear time-fractional Fornberg-Whitham equations using the Sumudu transform iterative method (STIM) within the Caputo fractional operator. The obtained solutions are illustrated graphically and demonstrate strong agreement with the exact solutions. The accuracy and reliability of the proposed method are further validated through comparisons with the Elzaki residual power series method (ERPSM) and the natural Adomian decomposition method (NADM) using absolute error analysis.
  Keywords: Sumudu transform; iterative method; time-fractional Fornberg-Whitham equation; Caputo fractional derivative.
  DOI: 10.1504/IJMMNO.2028.10078338
   
  
• A mathematical model of investment charges and switch costs imposed by two firms  
  by Anastasios Tsoularis, Paul.S Jones 
  Abstract: The dynamic interaction between two firms is investigated Each firm charges its customers a fixed joining fee and a fixed switch cost for switching to the other firm In addition, each firm charges an ongoing fee which plays the role of the dynamic variable The time evolution of the two dynamic variables is represented by an autonomous planar dynamical system. There are five exogenous parameters involved in the two-dimensional dynamics, two quantifying the demand for the firms’ services in terms of customer investment returns, and another three, capturing the probability of a good investment return, the degree of customer loyalty and the return itself. The five exogeneous parameters are identical for both firms. A detailed stability analysis is undertaken for all three different equilibria. The effect of the exogenous parameters on the stability of the equilibria is also examined.
  Keywords: centre manifold theorem; Lyapunov function; Bendixson criterion; Dulac function; Kolmogorov equations.
  DOI: 10.1504/IJMMNO.2028.10078557
   
  
• Applications of the generalised Bernoulli method to variational problems expressed in the Hamiltonian formalism  
  by Uriel A. Filobello-Nino, Hector Vazquez-Leal, Mario A. Sandoval-Hernandez, Cristian Dumay Hernandez-Garcia, Victor Manuel Jimenez-Fernandez, Rogelio A. Callejas-Molina, Roberto Ruiz-Gomez 
  Abstract: This work extends the generalised Bernoulli method (GBM) to the Hamiltonian formulation of variational problems, providing a systematic alternative to the Legendre transformation. Using only elementary calculus and differentiation with respect to incremental variables, our method directly yields canonical momenta and the energy function, which together define the Hamiltonian. Its effectiveness is shown through four examples: the harmonic oscillator, a bead on a rotating wire, a charged particle in an electromagnetic field, and the brachistochrone. In each case, GBM reproduces the Hamiltonian and Hamilton’s equations with minimal computational effort and exact agreement with standard formulations. For the brachistochrone, the method also yields the Hamilton-Jacobi equation and an explicit solution. By reducing formal complexity to an algebraic procedure, GBM preserves its strengths in the Euler-Lagrange setting while broadening applicability to systems with multiple coordinates, highlighting its value as a practical tool for Hamiltonian analysis in variational calculus.
  Keywords: generalised Bernoulli method; GBM; variational problems; Euler equations; Hamiltonian function; Hamilton-Jacobi equation; HJE.
  DOI: 10.1504/IJMMNO.2028.10078866
   
  
• PbMO-MFO: a metaheuristic approach integrating Pareto dominance into moth-flame optimisation  
  by Sunaina Mahant, Saurabh Srivastava, Alok Kumar 
  Abstract: Metaheuristic optimisation has emerged as a crucial method for solving challenging real-world problems, particularly in high-dimensional and multi-objective search spaces. The complex swarm intelligence technique known as Pareto-based multi-objective moth-flame optimisation (PbMO-MFO) was inspired by the transverse orientation behaviour of moths. The PbMO-MFOA finds a good balance between diversification and intensification by using a logarithmic spiral movement mechanism and a dynamic flame reduction technique. This prevents premature convergence and maintains search diversity. The algorithmic structure, convergence qualities, mathematical formulation, and comparative performance of PbMO-MFOA in relation to benchmark and real-world problems for optimisation are all covered in this study. The results indicate that PbMO-MFOA outperforms other modern metaheuristics regarding computational time and convergence rate. PbMO-MFOA is a promising technique for usage in machine learning, engineering, and complex decision-making problems because of its enormous potential in multi-objective optimisation.
  Keywords: Pareto-guided multi-objective moth-flame optimisation; nature-inspired swarm intelligence; metaheuristic optimisation methods; Pareto dominance principle; logarithmic spiral flight mechanism.
  DOI: 10.1504/IJMMNO.2028.10078869