International Journal of Applied Nonlinear Science (13 papers in press)

Regular Issues

• Fuzzy inventory modelling: addressing uncertainty in economic order quantity analysis within nonlinear science  
  by Soumendra Kumar Patra, Pragyan Parimita Sarangi, Nirmal Kumar Routra, Alok Kumar Jagadev, Bijay Kumar Paikaray 
  Abstract: Generally, in deriving the solution of economic order quantity (EOQ) inventory model, we consider deterioration rate, holding cost and ordering cost as constant. But in the case of real life problems, the above case is not actually constant but slightly disturbed from their original crisp value. In this paper, fuzzy inventory model is developed considering deterioration rate, holding cost and ordering cost as fuzzy variables. Because in practice, it is not always easy to determine the rate of deterioration precisely. In most of the cases it is uncertain in nature; therefore, it becomes reasonable to consider the vagueness and uncertainty of deterioration rate in fuzzy environment. These variables are represented by trapezoidal membership function. The function principle is applied to obtain an optimum total fuzzy cost along with optimum order quantity and optimum shortage quantity.
  Keywords: fuzzy membership function; fuzzy deterioration rate; trapezoidal numbers; function principle; defuzzification.
  DOI: 10.1504/IJANS.2024.10066705
   
  
• Solving fuzzy fractional differential equations using fuzzy fractional fourth order Runge-Kutta method based on centroidal mean  
  by S. Luvis Savla, R. Gethsi Sharmila 
  Abstract: In applied sciences and engineering, fuzzy fractional differential equations (FFDEs) are a crucial topic. The objective of this research is to determine the approximate solution to FFDEs. In the Caputo notion, the fractional derivatives are regarded. The fuzzy fractional fourth order Runge-Kutta method based on centroidal mean (FFRK4CeM) is developed to solve fuzzy fractional initial value problems (FFIVPs). The fuzzy fractional fourth-order Runge-Kutta method and the fuzzy fractional fourth-order Runge-Kutta method based on centroidal mean can be compared. Graphical results show the symmetry between the solutions lower and upper -cut representations and satisfy the convex symmetric triangular fuzzy number. As the step size decreases, the approximate solution increasingly aligns with the result. Finally, the results indicate that the proposed method is user-friendly, precise, straightforward, and efficient for addressing both linear and nonlinear first-order finite initial value problems (FFIVP).
  Keywords: Mittag-Leffler function; Caputo fractional derivative; fuzzy fractional differential equations; FFDEs; fuzzy fractional initial value problem; FFIVP; fuzzy fractional fourth order Runge-Kutta; FFRK4; fuzzy fractional fourth order Runge-Kutta method based on centroidal mean; FFRK4CeM; triangular fuzzy number; Zadeh’s extension principle; linear triangular FFIVP; nonlinear triangular FFIVP.
  DOI: 10.1504/IJANS.2024.10067543
   
  
• A machine learning-based nonlinear system for optimising crop selection and ensuring agricultural prosperity  
  by Mamata Garanayak, Swagatika Tripathy, Subrat Kumar Parida, Monalisa Panda, Bijay Kumar Paikaray, Fatimun Nisha 
  Abstract: Our nations economic prosperity is significantly influenced by agriculture. Investments in agricultural research and extension have consistently demonstrated excellent rates of return in Asia and the Pacific. In light of the impending difficulties in politics, the environment, and the economy, the cultivation of particular crops at specific times remains the primary issue that needs to be resolved. In this work, we create a prototype for recommendations that will first speculate on the kind of crop a farmer can cultivate based on the type of soil and environmental conditions (temperature, moisture, and rainstorm). The recommendation system will suggest five additional crops that are comparable to the predicted crop following the prediction. Prototypes relied on machine learning that have been shown to be effectual for predicting the best harvest can be utilised to accomplish this. The crops are predicted and recommended by the prototype with an accuracy of about 99.09%.
  Keywords: cultivation; crop counsel prototype; precision agriculture; recommendation prototype.
  DOI: 10.1504/IJANS.2024.10067544
   
  
• Interpreted social graph traversal algorithms for enhanced recommendation precision and efficiency in computational applications  
  by Jayanta Mondal, Sandipan Pine, Bijay Kumar Paikaray, Amita Yadav, Shalu Mehta 
  Abstract: The social network recommendation algorithms focusing on two novel approaches: interpreted social breadth first search (BFS) and the interpreted social depth first search (DFS). These algorithms aim to enhance the recommendation process by leveraging insights from social network analysis, graph traversal techniques, and interpreted relevance measures. This investigation utilising a real dataset sourced from Amazon, we compare the performance of BFS and DFS against conventional recommendation methods such as item-based collaborative filtering and hybrid approaches. This research finding reveals that BFS and DFS not only exhibit commendable precision but also demonstrate superior efficiency in terms of runtime. Moreover, our analysis indicates that these algorithms effectively narrow down the search space within the dataset, contributing to computational savings. This report sheds light on the potential of integrating social network structures and Interpreted user profiles into recommendation systems, offering valuable insights for researchers and practitioners in the field of recommender systems.
  Keywords: social network analysis; recommender systems; graph searching algorithms; user-based preferences; computational applications.
  DOI: 10.1504/IJANS.2024.10067729
   
  
• A fuzzy component technique for 3D convection-diffusion equation based on compact discretisation and exponential basis  
  by Navnit Jha, Kritika Gupta, Shivani Khandol 
  Abstract: This study introduces a fourth-order fuzzy component numerical technique incorporating compact discretisation, an exponential basis and fuzzy transform to solve 3D convection-diffusion equations. The proposed technique approximates the fuzzy components of the source function and solution representing mass transfer with an algebraic combination of seven and nineteen points respectively. This technique computes fourth-order accurate numerical solutions in the optimal time frame. The function approximation by fuzzy transform is estimated on an exponential basis, requiring the evaluation of free parameters. The value of free parameters is obtained in such a manner that the numerical scheme achieves sixth-order local truncation errors. This configuration yields a block tridiagonal matrix that optimises computation time and reduces the memory cost. By adjusting frequency parameters present on an exponential basis, an optimised numerical solution can be determined. The performance of the proposed technique is evaluated using a variety of convection-diffusion equations, along with the sine-Gordon equation. The techniques usefulness and efficiency are demonstrated by error bounds and their convergence order.
  Keywords: numerical computation; elliptic partial differential equation; fuzzy transform; triangular membership function; sine-Gordon equation; convection-diffusion equation; maximum absolute error.
  DOI: 10.1504/IJANS.2024.10068065
   
  
• Effect of heat transfer on swallowing through herniated oesophagus with dilating peristaltic wave amplitude  
  by Amirlal Singh, Shailendra Kumar Tiwari, Kirti Kumar Jaiswal 
  Abstract: The present study investigates the heat transfer effect on swallowing through herniated oesophagus. Due to the sliding hiatus hernia oesophagus gets diverged and then converged at the distal end. The wave propagating along the wall of the tube is sinusoidal with exponentially increasing wave amplitude. The pressure distribution within the oesophagus is computed numerically using a C++ program. The impact of the Grashof number and the heat source/sink parameter on pressure and wall shear stress have been discussed and physically interpreted. It is observed when either of the parameters increases the pressure along the oesophageal axis decreases. The pressure requirement to transport fluid in converging region is more unlike to diverging region. One more interesting result is that pressure is affected in proximal region also, although tube divergence and convergence occur near the distal end. These findings are significant to understand the physiological flow in the oesophagus under pathological conditions.
  Keywords: oesophagus; sliding hiatus hernia; peristalsis; dilating wave amplitude; Grashof number; heat transfer.
  DOI: 10.1504/IJANS.2024.10068664
   
  
• 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
   
  
• Nonlinear dynamics in wireless sensor networks: a comparative study of intelligent optimisation algorithms for hole detection and recovery  
  by Sonia Rathee, Shalu Mehta, Amita Yadav, Bijay Kumar Paikaray 
  Abstract: A wireless sensor network (WSN) is a dispersed sensor system to observe some physical or environmental conditions like temperature, pressure, sound, etc. The efficiency of ample numbers of sensors is employed to guarantee certain degree of redundancy in the coverage. This generates a need to implement some ideal sensor deployment scheme for even distribution of work load among sensors. Various optimisation algorithms are utilised to achieve the efficient deployment of sensor nodes in WSN. The essential functionalities of WSN cause the anomalies that occur in different types of holes in the network. The coverage holes are one of the anomalies affecting the operational efficiency of the sensor nodes of the WSN system. The research work is based on comparative study of coverage hole detection and void recovery protocols in WSN. The contribution of optimisation methods in hole detection and recovery is stated through studying the various researches.
  Keywords: wireless sensor network; WSN; coverage hole detection; hole recovery; optimisation; swarm intelligence.
  DOI: 10.1504/IJANS.2024.10069213
   
  
• Expansion formula for generalised q-Mittag-Leffler function using Leibniz rule  
  by Mulugeta Dawud Ali, Daya Lal Suthar 
  Abstract: In recent research, we have explored specific applications of the q-Leibniz rule. Through our investigations, we derived several intriguing transformations and expansions that involve various basic hypergeometric functions. These functions operate with one or more variables and include the fundamental analogue of Foxs H-function. This research papers explore novel expansion formulas that combine Foxs H-function with the generalised q-Mittag-Leffler function. By using the Leibniz rule to the q-Riemann and Weyl derivatives, these formulas derived more easily and open up new directions in mathematical analysis. Additionally, the study explores particular cases and uses arising from our primary finding, providing more context and understanding of the significance and usefulness of these expressions.
  Keywords: q-Gamma function; q-Mittag-Leffler function; Leibniz rule; Riemann Liouville q-derivative; Weyl q-derivative.
  DOI: 10.1504/IJANS.2024.10069489
   
  
• Numerical approximation of generalised time fractional KdV equation on bounded domain  
  by Kamlesh Kumar, Awadhesh K. Pandey 
  Abstract: We discuss a finite difference scheme (FDS) for the model of Korteweg-de Vries (KdV) equation with new generalised temporal fractional derivative over bounded domain. The generalised fractional derivative (GFD) containing scale and weight functions essentially redefines new derivative for a broader class of functions. Theoretical study shows that the fractional KdV model defined on bounded domain processes dissipative property when Dirichlet boundary condition is employed. The stability and convergence of FDS are also established. Validation of theoretical analysis is shown by two numerical simulations. The numerical findings are shown via tables and figures. The effect of scale function which is appears in GFD is also presented.
  Keywords: generalised fractional derivative; GFD; finite difference scheme; FDS; KdV equation.
  DOI: 10.1504/IJANS.2024.10069561
   
  
• A second order implicit-explicit general linear method based on continuous interpolants  
  by Sakshi Gautam, Ram K. Pandey 
  Abstract: Implicit-explicit (IMEX) general linear method (GLM) is a special class of GLM that solves differential systems containing both non-stiff and stiff parts. In the present paper, we present the continuous extension of an IMEX GLM of order two and stage order two. We derive the governing order conditions for IMEX-GLM using continuous interpolants. The proposed scheme is constructed using the continuous extension of the explicit counterpart of IMEX-GLM. Numerical examples of three partitioned (containing both the non-stiff and stiff parts) systems of problems in differential equations have been given to demonstrate the effectiveness of the second-order IMEX GLM based on continuous interpolants. The reported results reveal a good agreement between the reference solution and the numerical solution, and no order reduction is noticed for the proposed second-order method. Also, CPU time in seconds is calculated and reported in tables, which reflect the cost efficiency of the proposed scheme.
  Keywords: implicit-explicit solver; general linear method; GLM; continuous extension; order conditions; time-dependent partitioned nonlinear differential equations.
  DOI: 10.1504/IJANS.2024.10069641
   
  
• Multi-parametric analysis of chaotic dynamic behaviour of the Alpazur oscillator  
  by Aristide Dingamadji, Philippe Djondiné, Golam Guidkaya, Kriga Adoum 
  Abstract: In this paper we consider an Alpazur oscillator which consists of a Rayleigh-type oscillator and a DC power supply controlled by a switch that modifies the operating mode. The oscillator denotes some special phenomena in some parameters settings and is called chaos or bifurcation. In addition, we observe the behaviour of this oscillator over a wide range of parameter variation. Chaos theory tools such as, bifurcation, phase portrait, Poincar
  Keywords: Alpazur oscillator; switching operation; multi-parametric bifurcation; matching energy.