Advances in Mathematical Modelling, Applied Analysis and Computation: Proceedings of ICMMAAC 2021 (Lecture Notes in Networks and Systems, 415)

This book is a valuable source for graduate students and researchers and provides a comprehensive introduction to recent theories and applications of mathematical modeling and numerical simulation. It includes selected peer-reviewed papers presented at the 4th International Conference on Mathematical Modelling, Applied Analysis and Computation (ICMMAAC 2021), held at JECRC University, Jaipur, India, during August 5–7, 2021. The book is focused on mathematical modeling of various problems arising in science and engineering and new efficient numerical approaches for solving linear nonlinear problems and rigorous mathematical theories, which can be used to analyze different kinds of mathematical models. Applications of mathematical methods in physics, chemistry, biology, mechanical engineering, civil engineering, computer science, social science, and finance are presented. Preface Contents Editors and Contributors A Collection of Hilfer Fractional Opial Inequalities 1 Background 2 Main Results 2.1 Results Involving One Function 2.2 Results Involving Two Functions 2.3 Results Involving Several Functions References On a Non-linear Diffusion Model of Wood Impregnation: Analysis, Approximate Solutions, and Experiments with Relaxing Boundary Conditions 1 Introduction 1.1 Wood Impregnation: Main Factors Affecting the Process 1.2 Kowalski's Model 1.3 Kowalski's Model: Some Comments 1.4 Fokas' Solution Approach 1.5 Some Comments and Aim 1.6 Chapter Organization 2 Integral-Balance Solutions and Related Model Transformations 2.1 Integration Techniques 3 Approximate Solutions 3.1 Dirichlet Boundary Condition 3.2 Relaxing Dirichlet Boundary Conditions 3.3 Penetration Depth and Applicability of the Selected Relaxing Functions 4 Final Comments References Algorithmic Complexity-Based Fractional-Order Derivatives in Computational Biology 1 Introduction 2 Biological Dataset and Methodology 2.1 Diabetes Dataset 2.2 Methodology 3 Experimental Results and Discussion 3.1 Application of Mittag-Leffler Functions with Heavy-Tailed Distributions' Algorithm for Data Fitting Purposes 3.2 Application of Caputo Fractional-Order Derivatives with Three Parametric Mittag-Leffler Functions to Diabetes Dataset 3.3 Application of ANN Algorithm to Diabetes Dataset and Results 3.4 The Application of Algorithmic Complexity Based on Caputo Fractional-Order Derivative to the Diabetes Dataset 4 Conclusions, Outcomes and Future Directions References Case Study of Non-singular Kernel Model for MHD Boundary Layer Flow of a Rate Type Fluid over an Oscillating Plate 1 Introduction 2 Problem Description 3 Investigation of the Solution of the Problem 3.1 Investigation of the Solution of the Temperature 3.2 Investigation of the Solution of the Velocity 4 Limiting Solutions 4.1 Ordinary Maxwell Model ( αrightarrow1) 4.2 Fractional Viscous Fluid ( λ=0) 4.3 Viscous Fluid (αrightarrow1) 5 Graphical Description and Discussion of the Results 6 Final Remarks References Multilayer Perceptron Artificial Neural Network Approach to Solve Sixth-Order Two-Point Boundary Value Problems 1 Introduction 2 Structure of MLP ANN 3 Description of MLP ANN Technique 4 Numerical Results 5 Conclusion References Wavelet Transform on Generalized Quotient Spaces and Its Applications 1 Introduction 2 Generalized Quotient Spaces 3 Uniqueness Theorem for Wavelet Transform for Generalized Quotients of Analytic Functions 4 Wavelet Transform on Generalized Quotients in Lebesgue Space 5 Wavelet Transform on mathcalBmathcalS'(Td) 6 Conclusions References Certain Image Formulae of the Incomplete I-Function Under the Conformable and Pathway Fractional Integral and Derivative Operators 1 Introduction and Preliminaries 2 Main Results 3 Pathway Fractional Integral Formula 4 Particular Cases 5 Concluding Remarks References Explicit Exact Solutions and Conservation Laws of Modified α Equation 1 Introduction 2 Symmetry Analysis 3 Exact Solutions 3.1 Special Case: b=1, c=1 4 Conservation Laws 5 Results and Discussions 6 Conclusion References Some Approximation Results on Durrmeyer Modification of Generalized Szász–Mirakjan Operators 1 Introduction 2 Local Approximation Properties 3 Asymptotic Behaviour of the Operators 4 Quantitative Approximation 4.1 Grüss Voronovskaya Type Theorem References Fuzzy Approach to Solve General De-Novo Programming Problem 1 Introduction 1.1 Research Gap 1.2 Novelty 2 Proposed Approach for Solving GDNPP 2.1 Solution of MODNPP Using Zimmermann’s Non-compensatory Operator λ 2.2 Proposed Method 2.3 Algorithm 3 Numerical Example 4 Conclusion References Comparative Study of Eight Classification Models for Diagnosis and Prediction of Breast Cancer 1 Introduction 2 Literature Review 3 Data Mining Techniques 3.1 Logistic Regression (LR) 3.2 Decision Tree Classifier (DT) 3.3 Random Forest (RF) 3.4 Support Vector Machine (SVM) 3.5 K-Nearest Neighborhood (K-NN) 3.6 Artificial Neural Network (ANN) 3.7 Gaussian Naïve Bayes (NB) 3.8 AdaBoost Classifier 4 Results and Discussion 4.1 Data Pre-processing 4.2 Results and Discussion 5 Conclusion References Mathematical Model for Demonetization 1 Introduction 2 Model Formulation 2.1 The Positivity of Solutions 2.2 The Boundedness of Solutions 3 Equilibrium Points 3.1 Demonetization Free Equilibrium (DFE) 3.2 Demonetization Existence Equilibrium (DEE) 4 The Basic Reproduction Number (mathcalR0) 5 Stability Analysis 5.1 The Local Stability of the System 5.2 Local Stability of the DFE 6 Conclusion References An Inflationary Demand Scheme with Pareto Deterioration in Two Warehouses 1 Introduction 2 Assumptions and Notations 2.1 Assumptions 3 Mathematical Formulation 4 Solution Procedure of the Model 5 Numerical Example 6 Sensitivity Analysis 7 Conclusion References Exact Solitary Wave Solutions of the (3+1)-Dimensional Generalised Kadomtsev–Petviashvili Benjamin–Bona–Mahony Equation 1 Introduction 2 Preliminaries 3 Description of Modified Hyperbolic Function Expanding Method 4 Solutions of the (3+1)-Dimensional Generalised Kadomtsev–Petviashvili Benjamin–Bona–Mahony (KP-BBM) Equation 5 Numerical Results and Graphical Interpretation 6 Conclusion References Effect of Oblique Magnetic and Electric Fields on the Kelvin-Helmholtz Instability at the Interface Between Porous and Fluid Layers 1 Introduction 2 Mathematical Formulation 3 Problem Solution 3.1 Basic State Solutions 3.2 Perturbed Sate Equation 4 Dispersion Relation 4.1 Effect of Transverse Fields 4.2 Effect of Horizontal Fields 5 Results and Discussions 6 Conclusions References Heat Transfer for MHD Flow in an Inclined Channel with Heat Generation/Absorption 1 Introduction 2 Mathematical Formulation 3 Results and Discussions References Volterra Equation with Constant Fractional Order and Variable Order Fractal Dimension 1 Introduction 2 Fundamental Properties 2.1 Properties for the Case of Exponential Decay 3 Existence and Uniqueness 4 Numerical Schemes 5 Concluding Remarks References On the Parabolic Instability Region for Kuo Problem 1 Introduction 2 Kuo Problem 3 Parabolic Instability Region 4 Growth Rate 5 Concluding Remarks References Font Design Through RQT Bézier Curve Using Shape Parameters 1 Introduction 2 Methodology 2.1 Quintic Trigonometric Blending Functions 2.2 RQT Bézier Curve 2.3 Geometric Importance of Shape Parameters 2.4 Endpoint Curvatures Through Shape Control 3 Results and Discussion 3.1 Piecewise RQT-Bézier Curves 3.2 Two RQT-Bézier Curves Using C1 and G1 Continuity 3.3 Two RQT-Bézier Curves Using C2 and G2 Continuity 3.4 Font Design Using RQT-Bézier Curve 4 Conclusions References Effect of Partial Slip on Peristaltic Transport of MHD-Carreau Fluid in a Flexible Channel with Non-uniform Heat Source and Sink 1 Introduction 2 Construction of Governing Equations 2.1 Multi-step Differential Transformation Method 2.2 Method of Solution 3 Results and Discussion 3.1 Velocity Profile 3.2 Temperature Profile 3.3 Concentration Profile 3.4 Impact of Phycical Parameters 4 Conclusion References Invariant Preserving Schemes for Multi-symplectic Integrator of Two Long Waves’ Interactions 1 Introduction 2 Multi-symplectic Integrator of Two Long Waves’ Interactions 3 Conservation Property for Multi-symplectic Integrators 4 Numerical Simulations 5 Results and Discussion References Study of Effect of Overlapping Stenosis on Flow Field Considering Non-Newtonian Reiner Rivlin Blood Flow in Artery 1 Introduction 2 Formulation of Problem 3 Solution of Reiner Rivlin Model by Perturbation Method 4 Numerical Results and Discussion 5 Conclusions References Pathway Fractional Integral Formulae Involving Extended Bessel-Maitland Function in the Kernel 1 Introduction and Preliminaries 2 Pathway Fractional Integral Operator of an Extended Generalized Bessel-Maitland Function 3 Concluding Remarks References Analytical Approximate Approach to the Helmholtz-Duffing Oscillator 1 Introduction 2 Conservative Helmholtz-Duffing Oscillator 3 Solution Method 4 Results and Discussions References Haar Wavelet Series Method for Solving Simultaneous Proportional Delay Differential Equations 1 Introduction 2 Basic Definitions 2.1 Wavelet 2.2 Haar Wavelet 3 Description of Method 4 Algorithm 5 Implementation of Method on Test Problems 6 Conclusion References Fractional Reaction–Diffusion Model: An Efficient Computational Technique for Nonlinear Time-Fractional Schnakenberg Model 1 Introduction 2 Preliminaries 3 The Solution Procedure for the q-Homotopy Analysis Transform Method (q-HATM) 3.1 Solution for Non-linear Fractional Schnakenberg Model: 4 Numerical Results and Discussion 5 Conclusion References Existence of Salvage Value in a Memory Dependent EOQ Model in Absence of Deteriorating Items 1 Introduction 1.1 A Subsection Sample 2 Classical Inventory Model 2.1 Classical Model Formulation 3 Fractional-Order Inventory Model 3.1 Solution of the Fractional-Order Inventory Model 4 Numerical Example 5 Sensitivity Analysis 6 Conclusion References A Fuzzy Decomposable Approach for Posfust Reliability Evaluation of a Repairable Substation Automation System 1 Introduction 2 Basic Definitions 2.1 Fuzzy Set 2.2 Reliability 2.3 Availability 3 Decomposed Fuzzy Number 3.1 Methodology 4 Mathematical Formulation for Fuzzy Reliability and Availability 4.1 Equivalent Transition Rate 4.2 Fuzzy Reliability 5 Proposed Algorithm for the Automated System 6 Diagram of Automated System 7 Numerical Computations 7.1 Failure/Repair Rate Estimation 7.2 Evaluation of Possibility Measure and Necessity Measure 7.3 Calculation and Interpretation of Fuzzy Reliability 8 Conclusion 9 Data Availability Statement References Solution of Fingering Phenomenon Arising in Porous Media in Horizontal Direction by Combination of Elzaki Transform and Adomian Decomposition Method 1 Introduction 2 Mathematical Structure 3 Solution of Problem by Elzaki Adomian Decomposition Method 4 Convergence Analysis 5 Results and Discussion 6 Concluding Remarks References Numerical Study of Melting Impact on MHD Non-Newtonian Casson Fluid Flow Ran on a Stretching Sheet in a Porous Medium with Radiation and Dissipation Effect 1 Introduction 2 Formulation 3 Result and Discussion 4 Conclusion References Impact of Hall Current and Rotation on Unsteady MHD Oscillatory Dusty Fluid Flow Through Horizontal Porous Plates 1 Introduction 2 Mathematical Formulation 3 Solution of the Problem 4 Graphical Results and Discussions 5 Tables and Discussions 6 Conclusion References Study of Aligned MHD Casson Fluid Past a Shrinking Sheet with Viscous Dissipation 1 Introduction 2 Materials and Methods 3 Results and Discussion 4 Conclusions References Spin Coating of Non-Newtonian Nanofluid with Silver and Copper as Nanoparticle 1 Introduction 2 Mathematical Analysis 3 Numerical Solution 4 Result and Discussion References Analysis of Soret and Dufour Effect on MHD Fluid Flow Over a Slanted Stretching Sheet with Chemical Reaction, Heat Source and Radiation 1 Introduction 2 Mathematical Formulation of the Model 3 Numerical Procedures 4 Result and Discussion 5 Conclusions References Entropy Generation in Fourth-Grade Fluid Flow with Variable Thermal Conductivity 1 Introduction 2 The Problem 3 Solution Technique 4 The Entropy Generation Analysis 5 Result and Discussion 6 Conclusion References Solution of Nonlinear Fractional Differential Equation Using New Integral Transform Method 1 Introduction, Background and Preliminaries 2 Definition and Preliminary of Fractional Calculus and Elzaki Transform 3 Methodology of New Integral Transform [NIT] 4 Application of Elzaki Transform Method 5 Conclusion References Author Index