Advances in Mathematical Modelling, Applied Analysis and Computation. Proceedings of ICMMAAC 2021

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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