International Journal of Applied Nonlinear Science (19 papers in press)

Regular Issues

• Nonlinear modelling for precision farming: a deep learning ensemble approach to crop recommendation under variable soil and climate conditions  
  by Swagatika Tripathy, Premansu Sekhara Rath, Dibya Ranjan Das Adhikary, Bijay Kumar Paikaray 
  Abstract: Farming, which includes soil tilling, livestock raising, and food production, is a critical component of economic development, especially in agriculturally reliant countries. Farming, by providing food, raw materials, and job opportunities, is an essential basis for guaranteeing food security and maintaining livelihoods in both rural and urban areas. By accurately acknowledging the activities that need to be administered during the proper season, precision farming contributes to a rise in productivity. This study introduces a new recommendation system on a deep learning (DL)-based ensemble classifier for suggesting a suitable crop depending on location-specific soil and climatic conditions. The plan uses DL classifiers like ANN, CNN, RNN, LSTM, and CRNN to classify and recommend crops. Then afterward, an ensemble model (meta-classifier) is used to propose a better crop depending on different factors with better accuracy. The overall accuracy of the ensemble model is 97.69%. The evolution of crop recommendations using DL can help farmers enhance crop yields, increase agricultural sustainability, and meet the worldwide requirement for food.
  Keywords: nonlinear; deep learning; crop recommendation; soil characters; climatic characteristics; agricultural sustainability; soil and climatic; meta-classifier.
  DOI: 10.1504/IJANS.2024.10068906
   
  
• Modelling the vertical and horizontal transmission dynamics of HIV infection  
  by Arvind Kumar Sinha, Sunil Kanhaiyalal Kushavaha 
  Abstract: HIV remains a significant global public health issue, with mother-to-child transmission responsible for 20% of all HIV transmissions. HIV can be transferred vertically during pregnancy, childbirth, or breastfeeding. In this study, we introduced a mathematical model of HIV/AIDS on aware and unaware infected populations with vertical transmission and control measures. We demonstrate the boundedness and positivity of the model, identify the equilibrium points, and analyse their stability. We illustrate the effects of parameters through numerical simulations. Sensitivity analysis reveals the correlation between parameters and the reproduction number. We introduce an optimal control model with obstructing the vertical transmission route, the intensity of screening latent population, and treatments of aware infected populations. We obtain the most effective strategy involves obstructing the vertical transmission route and the intensity of screening the latent population. This research will aid in supporting the United Nations goal of preventing HIV/AIDS both vertically and horizontally.
  Keywords: stability analysis; sensitivity analysis; optimal control; HIV/AIDS; HIV in pregnancy.
  DOI: 10.1504/IJANS.2025.10069171
   
  
• Content-based retinal image analysis for diabetic retinopathy detection using local neighbouring texture features  
  by Arpita Santra, Vibhav Prakash Singh, Roshan Singh 
  Abstract: This study explores diabetic retinopathy (DR) classification and retinal image retrieval using machine learning (ML) algorithms, emphasising feature extraction through local binary patterns (LBP) and local ternary patterns (LTP) with various radius values. Among the ML models tested, random forest achieved the highest classification accuracy of 94%, outperforming support vector machines (SVM) and decision trees. For retinal image retrieval, combining LBP and LTP features with a radius of three yielded superior results, especially when enhanced by CLAHE pre-processing. The study also evaluated feature selection methods, finding that the combined LBP-LTP approach without feature selection delivered the best outcomes. These findings highlight the effectiveness of integrating LBP and LTP features for both DR classification and image retrieval, offering a promising solution for enhancing retinal image analysis and improving diagnostic accuracy.
  Keywords: fundus images; diabetic retinopathy; feature selection; local binary pattern; LBP; local ternary pattern; LTP.
  DOI: 10.1504/IJANS.2025.10069929
   
  
• Exploring steady-state creep deformation in an externally pressurised orthotropic rotating cylinder: a comprehensive investigation  
  by Priya Gulial, Pankaj Thakur 
  Abstract: This paper explores steady-state creep analysis in an orthotropic rotating cylinder subjected to external pressure. Creep behaviour is studied using Norton's law. Numerical computations were conducted for various steels and steel alloys, covering five distinct types of anisotropy. The research highlights the effects of anisotropy and the exponent 'n' in the creep law. Strain rates decrease near the cylinder's inner surface, with type 5 exhibiting the highest circumferential strain and type 1 the lowest. Type 4 requires more strain than type 2, with type 3 in between. Radial strain rates exhibit reversed results.
  Keywords: pressure; cylinder; angular speed; anisotropic; isotropic.
  DOI: 10.1504/IJANS.2025.10070431
   
  
• Cannibalism, harvesting and disease: complex interactions in ecological model  
  by Deepak Tripathi, Anuraj Singh, Preeti Deolia 
  Abstract: The present study explores the complex interactions between prey and cannibalistic predators in the context of infection dynamics, incorporating the role of harvesting as a control mechanism. Using dynamical systems theory, we investigate the behaviour of a predator-prey system where the predator population is susceptible to disease. We provide a rigorous mathematical and numerical analysis of the systems equilibria, including trivial, predator free, disease free, and interior steady states alongside their stability. Our findings highlight that increased cannibalism among predators suppresses oscillatory behaviour in the system, while the introduction of harvesting enhances the population of non-infected predators. Additionally, we demonstrate that the system undergoes a Hopf bifurcation under specific conditions, leading to periodic solutions. This work presents a comprehensive integration of harvesting, cannibalism, and infection dynamics into a single framework, offering new insights into ecological management and disease control strategies.
  Keywords: cannibalism; disease; harvesting; basic reproduction number; Hopf bifurcation.
  DOI: 10.1504/IJANS.2025.10071798
   
  
• Subpopulation compartmental mathematical model for viral disease transmission among diabetic and non-diabetic population  
  by Tejaswi Kadam, V.R. Nikam 
  Abstract: The paper aims to formulate and analyse a compartmental mathematical model for viral disease transmission, focusing on diabetic and non-diabetic subgroups. Subpopulation SIR model describing interactions between individuals who are susceptible, infected, and recovered is formulated. Existence and stability of a disease-free equilibrium are studied. Final size relation of an epidemic is derived. Basic reproduction number is computed by using the next-generation matrix method. Sensitivity analysis is carried out to determine relative importance of the different parameters influencing the final size of an epidemic and the basic reproduction number. We performed numerical simulations to support the analytical results. The effect of implementing public health measures such as prioritised vaccination and isolation is discussed. Obtained results that disease spread dynamics, and estimated basic reproduction number are sensitive to susceptibility and recovery rate parameters, which differ for the diabetic and non-diabetic populations, are valuable for preparing public health measures to combat epidemics.
  Keywords: heterogeneity; epidemic; viral disease; comorbidities; diabetic; subpopulation model; reproduction number; sensitivity analysis.
  DOI: 10.1504/IJANS.2025.10072316
   
  
• Impact of maturation delay on prey-predator model with hunting cooperation  
  by Krishnanand Vishwakarma, Mithilesh Kumar Chaube 
  Abstract: In ecology, the hunting cooperation among predators is one of the important natural phenomena which addresses the many mechanisms during the hunting. The study of hunting cooperation with maturation delay is not much studied as per the literature point of view. In the current paper, we consider a delayed prey-predator system with hunting cooperation. The main aim of this paper is to address how the system stabilised by introducing a maturation delay under the considering model. While, destabilisation is a common finding that results in most of the prey-predator models, whenever the discrete time delay is induced in the system. Here, for the sake of simplicity, we consider a linear functional response which depends on both prey and predator densities. We also provide the feasible conditions for the co-existence of the population species. Further, we investigated the stability of coexisting equilibria and the existence of Hopf-bifurcation is carried out when the maturation delay parameter crosses some critical magnitude referred 0 with one parameter bifurcation. Finally, the ecological significance of observations is discussed in the conclusions section.
  Keywords: delay differential equation; DDE; functional response; hunting cooperation; stability; bifurcations.
  DOI: 10.1504/IJANS.2025.10072424
   
  
• An analysis of a system of rational difference equations of order six  
  by Stephen Sadiq, Muhammad Shabbir, Shahid Nisar, Wizda Iqbal, Lubna Mustafa 
  Abstract: In this paper, we study the form of solutions, the equilibrium point, the boundedness, convergence, and the periodic nature of a discrete dynamical system defined by the system of rational difference equations with delayed indices. Furthermore, we provide several numerical examples to support and validate the theoretical findings, which not only confirm the analytical results but also highlight interesting dynamical behaviours.
  Keywords: rational difference equations; equilibrium points; boundedness; periodicity.
  DOI: 10.1504/IJANS.2025.10072596
   
  
• Simulation and analysis of hepatitis C virus with fractional approach  
  by Farhan Sarwar, Muhammad Shoaib Farooq, Muhammad Imran Asjad, Hafsa Manzoor 
  Abstract: Hepatitis C is a serious infectious disease responsible for approximately 326,000 cirrhosis-related and 167,000 liver cancer deaths annually. With around 170 million people infected globally and no vaccine available, prevention remains the most effective strategy. This study introduces a mathematical model for managing Hepatitis C to reduce infection rates in society. We focus on analysing recovery either natural or treatment-induced using a non-integer order model based on the Caputo fractional derivative. The model employs Laplace transform, Adomian polynomials for nonlinear components, and iterations of the homotopy perturbation method (HPM) to obtain semi-analytical solutions. MATLAB simulations validate our approach and compare model results with actual data. The numerical outcomes, grounded in the Laplace-Adomian and HPM techniques, demonstrate that the fractional-order model provides more accurate and optimal results than traditional integer-order methods. This modelling approach offers a robust framework applicable to various problems in applied sciences and engineering.
  Keywords: fractional-order hepatitis C virus model; singular Caputo operator derivative; Laplace Adomian decomposition technique; homotopy perturbation technique; semi-analytical solution; numerical solution.
  DOI: 10.1504/IJANS.2025.10073150
   
  
• Investigating the numerical behaviour of the time fractional Whitham-Broer-Kaup equation employing radial basis functions  
  by Harshad Sakariya, Sushil Kumar 
  Abstract: This study investigates the time fractional Whitham-Broer-Kaup equation, using radial basis functions for the spatial variable and the finite difference method for the temporal variable. The accuracy and reliability of the scheme are validated through a code verification procedure. Additionally, the absolute errors obtained from the present scheme are compared with those of other methods available in the literature to verify the proposed schemes efficacy. Approximate solutions for different parameters (c1 and c2) and various time-fractional orders are obtained, along with their effects on horizontal velocity and wave amplitude. The results are shown graphically to provide more precise insights into the studied phenomena.
  Keywords: time fractional; Whitham-Broer-Kaup equation; Caputo fractional derivative; radial basis functions; finite difference method.
  DOI: 10.1504/IJANS.2025.10073219
   
  
• Some estimates on one-sided generalised weighted like Morrey space  
  by Nishikesh Upadhyaya, Rajib Haloi 
  Abstract: The boundedness of the fractional maximal operator in various function spaces is studied by various authors. In this paper, we prove the boundedness of one-sided scalar-valued and vector-valued fractional maximal functions on one-sided generalised weighted like Morrey space. The relationships between some function classes are essential, which are also proved as lemmas in the paper. Some lemmas are also proved, which are essentially required in the proof of the main theorem. In the later part of the paper, we also prove the Fefferman-Stein type inequality in both scalar and vector-valued settings.
  Keywords: weight; Morrey space; maximal function; fractional maximal function; one-sided generalised weighted; weighted norm inequalities.
  DOI: 10.1504/IJANS.2025.10073527
   
  
• Advanced numerical methods for singular models via Vieta-Lucas wavelets  
  by Shivani Aeri, Rakesh Kumar, Dumitru Baleanu, Kottakkaran Sooppy Nisar 
  Abstract: This study discusses the computational methods used to solve singular differential equations numerically. Nonlinear singular differential equations are used to simulate many real-world problems. Solving singular differential equations is essential due to the presence of singularities. The proposed approaches utilise the Vieta-Lucas wavelets in combination with collocation, tau and Galerkin methods to improve the accuracy and efficiency of the numerical solutions. The operational matrix of the derivative is computed for Vieta-Lucas wavelets and utilised to transform the differential equations into a set of algebraic equations. In addition, the study of convergence and estimation of errors are thoroughly addressed. In the numerical part, the offered approaches are used to solve five individual models. There is a significant level of concurrence between the exact and approximate outcomes, and in some instances, the approximated values demonstrated remarkable precision.
  Keywords: Vieta-Lucas wavelets; generating function; Rodrigues’ formula; collocation method; Galerkin method; tau method.
  DOI: 10.1504/IJANS.2025.10074005
   
  
• A high-order adaptive numerical method for boundary layer-originated nonlinear problems with non-local boundary condition  
  by Shashikant Kumar, Sumit Sumit, Sunil Kumar 
  Abstract: The objective of this article is to present a high-order adaptive numerical scheme for boundary layer-originated nonlinear problems with a non-local boundary condition. The concerned problem is approximated using a high-order scheme on a non-uniform mesh. Then, an a posteriori error analysis for the approximations of the solution is given, based on which a suitable monitor function is chosen for adaptive grid generation using the mesh equidistribution principle. Convergence analysis proves that the presented scheme is second-order accurate in the maximum norm. Subsequently, numerical simulations are performed, and results illustrating the theoretical findings and demonstrating the effectiveness of the present a posteriori error estimate are presented.
  Keywords: boundary layers; adaptive numerical methods; hybrid scheme; integral equations; equidistribution principle; monitor function; nonlinear problems.
  DOI: 10.1504/IJANS.2025.10074443
   
  
• Qualitative analysis of a fractional integro-differential equation with constant delay with integral initial condition  
  by Sabita Bera, Mausumi Sen, Sujit Nath 
  Abstract: The Atangana-Baleanu fractional integro-differential equation models complex systems with memory effects across various fields such as diffusion, materials science, control systems, and finance. This article examines a specific Volterra-type integro-differential equation (IDE) that incorporates the Atangana-Baleanu fractional derivative in the Caputo sense (ABFDC). First, we have established the conditions for the existence of a solution using Schauders fixed point theorem (FPT). Next, we have demonstrated the conditions for the uniqueness of the solution by applying the Banach fixed point theorem. Additionally, we have analysed the Ulam-Hyers stability of the fractional IDE. Finally, we have presented a numerical example to validate our theoretical findings.
  Keywords: integro-differential equation; fractional calculus; existence; uniqueness; Banach fixed point theory; Schauder’s fixed point theory.
  DOI: 10.1504/IJANS.2025.10074613
   
  
• Electrically conducting micropolar fluid flow past a wedge embedded in porous media  
  by Atul Kumar Ray, Amit Kumar, Dig Vijay Tanwar, Prashanta Kumar Mandal, B. Vasu, P. V. S. N. Murthy 
  Abstract: A fundamental engineering problem is investigated by studying the flow of electrically conducting non-Newtonian micropolar fluid from a porous wedge in presence of magnetic field and heat source/sink. The study is applicable to lubricating systems, wedge shape blocks, lift analysis, design of aerospace component, wedge shaped infarct and processing of polymers. By applying suitable transformations, the non-dimensional boundary value problem (BVP) is reduced to system of coupled nonlinear ordinary differential equations (ODEs). The temperature, primary and secondary velocity are computed to evaluate the impact of various key parameter (Hartmann number, Eringen micropolar parameter and heat sink parameter). Results show that with enhancement in wedge angle, the rotational effects within the micropolar fluid are decreased, leading to a lower wall couple stress. Primary velocity is reduced due to increase in MHD parameter. This decrease in primary velocity due to micro-inertial density parameter is key functional performance in applications such as optical coating, anti-corrosion or conductive coatings. Also, controlling the primary velocity is crucial to preclude early sedimentation. Higher the permeability, more fluid is absorbed into porous medium around the wedge, which slows down the main flow. Validation of the study is done with previously published articles.
  Keywords: micropolar fluid; wedge flow; heat transfer; boundary layers; Nusselt number; Hartman number; BVP4c.
  DOI: 10.1504/IJANS.2025.10074759
   
  
• An error-bounded approximation scheme for the results of Abels integral equations  
  by Ankit Kumar 
  Abstract: The current study develops an error-bounded approximation scheme for analysis the results to Abels integral equation (AIE) by applying modified Lucas wavelets (MLWs). The AIE serves as a crucial mathematical tool in engineering, particularly in solving inverse problems, analysing diffusion processes, and performing signal deconvolution. Its wide-ranging applications extend from thermal analysis to biomedical imaging, highlighting its significance in various scientific and technological advancements. Using the implemented scheme, the given AIE is transformed into an appropriate algebraic system by combining collocation points. In this paper, we employ the MLWs scheme to derive a new estimator for function belonging to Holder class. This approximation scheme aims to deliver rapid and efficient solutions for AIE. To guarantee accuracy, applicability, and stability, we conducted a series of examples and compared the outcomes with existing wavelet colocations methods. Our findings demonstrate that the proposed scheme consistently achieves superior results using a minimal number of wavelet basis functions. Furthermore, increasing the order of the wavelet basis enhances the accuracy of the Abel integral equation (AIE) solutions.
  Keywords: wavelets; collocation scheme; MLWs; AIE; function of Holder’s class.
  DOI: 10.1504/IJANS.2025.10074760
   
  
• Solvability and approximation of a nonlinear Hammerstein type Volterra quadratic integral equation  
  by Sukanta Halder, Deepmala Deepmala 
  Abstract: In this paper, we consider a generalised nonlinear Hammerstein type Volterra quadratic integral equation (HVQIE) and examine the sufficient conditions that guarantee the existence and uniqueness of a solution to this equation. After that, we analyse the Adomian decomposition method (ADM), a semi-analytical approach, for approximating solutions of HVQIE. The ADM is a highly effective tool for solving a wide range of functional integral equations. It provides valuable insights into nonlinear science and offers a reliable approach for robust computational techniques in numerous scientific and engineering areas. We also examine ADMs convergence analysis with the assistance of sufficient conditions and the Adomian polynomial formula. As a result, we estimate the Adomian series solutions maximum absolute truncated error. Furthermore, in special cases, our results include various functional integral equations. Finally, we offer some examples to validate our results in detail.
  Keywords: fixed point theory; FPT; Adomian decomposition method; ADM; convergence analysis.
  DOI: 10.1504/IJANS.2025.10075681
   
  
• Predictive analysis of NPA and loan assets of private sector banks in India  
  by P. Buvaneswari, V. Pushpalatha 
  Abstract: In this research paper, the authors employ statistical models to analyse the non-performing assets and loan assets of private sector banks in India. The aim is to examine the gross and net non-performing assets of these banks and propose methods to reduce non-performing assets and enhance the banks ability to systematically classify their loan assets. The research is based on secondary data and involves analytical research methods. The researchers will analyse the non performing assets and loan assets of private sector banks in India using statistical tools, with estimations performed through R-programming. The dataset comprises ten years of data, spanning from 201314 to 202223, on non performing assets and loan assets. The findings will determine the models that best fit the data
  Keywords: ability; systematically; analyse; models.
  DOI: 10.1504/IJANS.2025.10075683
   
  
• Mathematical exploration of optical solitons in the Lakshmanan-Porsezian-Daniel model using an analytical scheme  
  by Moazzama Faraz, Umair Asghar, Muhammad Imran Asjad 
  Abstract: This article investigates the Lakshmanan-Porsezian-Daniel (LPD) equation, an important nonlinear partial differential equation used to model optical pulse propagation in fibre media with higher-order nonlinear effects. By incorporating variable coefficients, the LPD equation accounts for self-phase modulation, self-steepening, and group-velocity dispersion, making it suitable for describing ultra-short optical pulses such as femtosecond and attosecond waves. The sub-equation method is employed to obtain exact travelling-wave solutions, including periodic solitons, anti-peakons, anti-kinks, and singular kinks. Various 2D and 3D profiles are presented to illustrate the physical behaviour under different parameter choices. This work is the first to apply the sub-equation method to the LPD equation, providing new solution structures not previously reported. The results contribute to nonlinear science and offer valuable insights for optical communication and higher-dimensional nonlinear wave phenomena.
  Keywords: Lakshmanan-Porsezian-Daniel equation; sub-equation method; soliton solutions; application in optics.
  DOI: 10.1504/IJANS.2025.10075981