Mathematical Modelling, Applied Analysis and Computation: ICMMAAC 2018, Jaipur, India, July 6-8 (Springer Proceedings in Mathematics & Statistics Book 272)

This book contains original research papers presented at the International Conference on Mathematical Modelling, Applied Analysis and Computation, held at JECRC University, Jaipur, India, on 6-8 July, 2018. Organized into 20 chapters, the book focuses on theoretical and applied aspects of various types of mathematical modelling such as equations of various types, fuzzy mathematical models, automata, Petri nets and bond graphs for systems of dynamic nature and the usage of numerical techniques in handling modern problems of science, engineering and finance. It covers the applications of mathematical modelling in physics, chemistry, biology, mechanical engineering, civil engineering, computer science, social science and finance. A wide variety of dynamical systems like deterministic, stochastic, continuous, discrete or hybrid, with respect to time, are discussed in the book. It provides the mathematical modelling of various problems arising in science and engineering, and also new efficient numerical approaches for solving linear and nonlinear problems and rigorous mathematical theories, which can be used to analyze a different kind of mathematical models. The conference was aimed at fostering cooperation among students and researchers in areas of applied analysis, engineering and computation with the deliberations to inculcate new research ideas in their relevant fields. This volume will provide a comprehensive introduction to recent theories and applications of mathematical modelling and numerical simulation, which will be a valuable resource for graduate students and researchers of mathematical modelling and industrial mathematics. Preface 6 Contents 11 Editors and Contributors 13 Certain Banach-Space Operators Acting on the Semicircular Elements Induced by Orthogonal Projections 18 1 Introduction 18 1.1 Motivations 19 1.2 Overview 20 2 Preliminaries 20 3 Fundamental Settings 20 4 Weighted-Semicircular Elements Induced by Q 25 5 Semicircular Elements Induced by Q 31 6 32 7 Shifts on mathbbZ and Integer-Shifts on mathbbLQ 37 7.1 (pm)-Shifts on mathbbZ 37 7.2 Integer-Shifts on mathbbLQ 38 7.3 Free Distributions on mathbbLQ Under the Action of mathfrakB 47 8 Actions of mathfrakB on mathbbLQ 51 9 Banach-Space Operators on mathbbLQ Preserving Free Probability 54 References 55 Explicit Expressions Related to Degenerate Cauchy Numbers and Their Generating Function 57 1 Motivations and Main Results 58 2 Lemmas 60 3 Proofs of Theorems 1 and 2 61 4 Remarks 65 References 66 Statistical Deferred Riesz Summability Mean and Associated Approximation Theorems for Trigonometric Functions 69 1 Introduction, Preliminaries and Motivation 70 2 A Korovkin-Type Approximation Theorem Based on Deferred Riesz Mean 73 3 Rate of the Statistical Deferred Weighted (Riesz) Summability 77 4 Conclusion 80 References 82 On Pointwise Convergence of a Family of Nonlinear Integral Operators 84 1 Introduction 85 2 Preliminaries 86 3 Existence of the Operators and Pointwise Convergence 87 4 Main Theorem 92 5 Rate of Convergence 95 References 97 Existence and Ulam's Type Stability of Integro Differential Equation with Non-instantaneous Impulses and Periodic Boundary Condition on Time Scales 99 1 Introduction 99 2 Preliminaries 101 3 Existence and Uniqueness 103 4 Hyer-Ulam's Stability 109 5 Example 114 6 Conclusion 115 References 115 Introduction to Class of Uniformly Fractional Differentiable Functions 117 1 Introduction 117 2 Uniformly Fractional Differentiable Functions 119 References 125 Asymptotically Almost Automorphic Solution for Neutral Functional Integro Evolution Equations on Time Scales 126 1 Introduction 126 2 Preliminaries 127 3 Main Result 132 4 Stability Result 137 5 Example 138 References 139 An Integral Relation Associated with a General Class of Polynomials and the Aleph Function 141 1 Introduction 141 2 Main Result 143 3 Special Cases 144 References 148 On the New Fractional Operator and Application to Nonlinear Bloch System 149 1 Introduction 149 2 Fractional Operators 151 3 Bloch System with Non-singular Kernel 151 4 Numerical Simulations 159 5 Conclusions 164 References 164 Fractional Order Integration and Certain Integrals of Generalized Multiindex Bessel Function 167 1 Introduction and Preliminaries 168 2 Fractional Calculus Approach of mathcalJ( βj) m,κ,b( αj)m,γ,c[ z] 169 2.1 Fractional Integration 169 2.2 Fractional Differentiation 171 3 Certain Integrals of the mathcalJ( βj) m,κ,b( αj)m,γ,c[ z] 173 4 Concluding Remark and Discussion 178 References 178 Fractional Variational Iteration Method for Time Fractional Fourth-Order Diffusion-Wave Equation 180 1 Introduction 180 2 Preliminaries 182 3 Description of Fractional Variational Iteration Method (FVIM) 183 4 Test Examples 183 5 Numerical Results and Discussions 185 6 Conclusion 187 References 188 Analytical Approach to Fractional Navier–Stokes Equations by Iterative Laplace Transform Method 190 1 Introduction 190 2 Some Basic Definitions 191 3 Basic Idea of ILTM 192 4 Solutions of the Time-Fractional Navier–Stokes Equations 194 5 Numerical Results and Discussions 197 References 199 Biological Model of Dengue Spread with Non-Markovian Properties 200 1 Introduction 200 2 Preliminaries 202 3 Model Description 203 4 Uniqueness and Existence of a System of Solutions of Dengue Models with Non-Markovian Properties 205 5 Numerical Solution 213 6 Numerical Simulation 215 7 Conclusion 218 References 218 Approximate Solution of Higher Order Two Point Boundary Value Problems Using Uniform Haar Wavelet Collocation Method 220 1 Introduction 220 2 Multiresolution Analysis and Haar Wavelet 221 3 Methods of Solution 223 3.1 Method for Solving Second Order Differential Equations 223 3.2 Method for Solving Fourth Order Differential Equations 224 4 Numerical Examples 226 5 Conclusion 231 References 231 Solving Multi-objective Fractional Transportation Problem 232 1 Introduction 232 2 Problem Description and Definitions 233 2.1 Mathematical Formulation of Multi-objective Linear Fractional Transportation Problem 233 2.2 Pareto Optimal Solution 234 3 Weighted Sum Method 234 4 Proposed Method 235 5 Numerical Examples 235 6 Conclusion 239 References 239 On the Dark and Bright Solitons to the Negative-Order Breaking Soliton Model with (2+1)-Dimensional 240 1 Introduction 240 2 General Properties of IBSEFM 241 3 Application of the IBSEFM 242 4 Conclusion 249 References 250 A Reliable Analytical Algorithm for Cubic Isothermal Auto-Catalytic Chemical System 254 1 Introduction 255 2 Basic Ideas of the q-HATM 256 2.1 Convergence Analysis 259 3 q-HATM solution of CIACS 259 4 Numerical Results 261 4.1 h-Curves 262 4.2 Average Residual Errors 263 4.3 Comparison Analysis 267 5 Conclusion 269 References 269 Numerical Study of Effects of Adrenal Hormones on Lymphocytes 272 1 Introduction 273 2 Formulation and Analysis of the Model Equations 273 2.1 Model Formulation 273 2.2 Model Analysis 274 3 Numerical Solution 279 3.1 Diffusion Model 279 3.2 Full Diffusion Model 281 4 Conclusion 284 References 284 Mathematical Modelling of Poor Nutrition in the Human Life Cycle 285 1 Introduction 285 2 Model Formulation 288 2.1 Model Diagram 288 2.2 Model Equation 288 2.3 Model Analysis 289 2.4 Analysis of Malnutrition Free Steady State 291 2.5 The Basic Reproduction Number 291 2.6 Stability Analysis of Steady States 292 2.7 Stability of Endemic Steady State 293 3 Numerical Simulation 295 3.1 Parameter Estimation 295 3.2 Sensitivity Analysis 295 4 Results 296 4.1 Simulation Results 296 5 Conclusion 301 References 302 Characteristics of Homogeneous Heterogeneous Reaction on Flow of Walters' B Liquid Under the Statistical Paradigm 304 1 Introduction 304 2 Formulation 306 3 OHAM 309 4 Optimal Convergence Control Parameters 310 5 Discussion 311 6 Statistical Paradigm 314 7 Probable Error (P.E.) 316 7.1 Statistical Proclamation 317 8 Conclusions 317 References 318 Front Matter ....Pages i-xvii Certain Banach-Space Operators Acting on the Semicircular Elements Induced by Orthogonal Projections (Ilwoo Cho)....Pages 1-39 Explicit Expressions Related to Degenerate Cauchy Numbers and Their Generating Function (Feng Qi, Ai-Qi Liu, Dongkyu Lim)....Pages 41-52 Statistical Deferred Riesz Summability Mean and Associated Approximation Theorems for Trigonometric Functions (M. Patro, S. K. Paikray, B. B. Jena, Hemen Dutta)....Pages 53-67 On Pointwise Convergence of a Family of Nonlinear Integral Operators (Gumrah Uysal, Hemen Dutta)....Pages 69-83 Existence and Ulam’s Type Stability of Integro Differential Equation with Non-instantaneous Impulses and Periodic Boundary Condition on Time Scales (Vipin Kumar, Muslim Malik)....Pages 85-102 Introduction to Class of Uniformly Fractional Differentiable Functions (Krunal B. Kachhia, Jyotindra C. Prajapati)....Pages 103-111 Asymptotically Almost Automorphic Solution for Neutral Functional Integro Evolution Equations on Time Scales (Soniya Dhama, Syed Abbas)....Pages 113-127 An Integral Relation Associated with a General Class of Polynomials and the Aleph Function (Monika Jain, Sapna Tyagi)....Pages 129-136 On the New Fractional Operator and Application to Nonlinear Bloch System (J. F. Gómez-Aguilar, Behzad Ghanbari, Ebenezer Bonyah)....Pages 137-154 Fractional Order Integration and Certain Integrals of Generalized Multiindex Bessel Function (K. S. Nisar, S. D. Purohit, D. L. Suthar, Jagdev Singh)....Pages 155-167 Fractional Variational Iteration Method for Time Fractional Fourth-Order Diffusion-Wave Equation (Amit Prakash, Manoj Kumar)....Pages 169-178 Analytical Approach to Fractional Navier–Stokes Equations by Iterative Laplace Transform Method (Rajendra K. Bairwa, Jagdev Singh)....Pages 179-188 Biological Model of Dengue Spread with Non-Markovian Properties (Sonal Jain, Abdon Atangana)....Pages 189-208 Approximate Solution of Higher Order Two Point Boundary Value Problems Using Uniform Haar Wavelet Collocation Method (Akmal Raza, Arshad Khan)....Pages 209-220 Solving Multi-objective Fractional Transportation Problem (Vishwas Deep Joshi, Rachana Saini)....Pages 221-228 On the Dark and Bright Solitons to the Negative-Order Breaking Soliton Model with (2+1)-Dimensional (Haci Mehmet Baskonus)....Pages 229-242 A Reliable Analytical Algorithm for Cubic Isothermal Auto-Catalytic Chemical System (Khaled M. Saad, H. M. Srivastava, Devendra Kumar)....Pages 243-260 Numerical Study of Effects of Adrenal Hormones on Lymphocytes (Shikaa Samuel, Vinod Gill, Devendra Kumar, Yudhveer Singh)....Pages 261-273 Mathematical Modelling of Poor Nutrition in the Human Life Cycle (Ebenezer Bonyah, Kojo Ababio, Patience Pokuaa Gambrah)....Pages 275-293 Characteristics of Homogeneous Heterogeneous Reaction on Flow of Walters’ B Liquid Under the Statistical Paradigm (Anum Shafiq, T. N. Sindhu, Z. Hammouch)....Pages 295-311