Applied Analysis, Optimization and Soft Computing: ICNAAO-2021, Varanasi, India, December 21–23

Description

This book contains select contributions presented at the International Conference on Nonlinear Applied Analysis and Optimization (ICNAAO-2021), held at the Department of Mathematics Sciences, Indian Institute of Technology (BHU) Varanasi, India, from 21–23 December 2021. The book discusses topics in the areas of nonlinear analysis, fixed point theory, dynamical systems, optimization, fractals, applications to differential/integral equations, signal and image processing, and soft computing, and exposes the young talents with the newer dimensions in these areas with their practical approaches and to tackle the real-life problems in engineering, medical and social sciences. Scientists from the U.S.A., Austria, France, Mexico, Romania, and India have contributed their research. All the submissions are peer reviewed by experts in their fields. Contents About the Editors Fixed Point Theory Large Contractions and Surjectivity in Banach Spaces 1 Introduction and Preliminaries 2 A Surjectivity Theorem for Single-valued Large Contractions 3 Multivalued Large Contractions References On Hick's Contraction Using a Control Function 1 Introduction and Mathematical Preliminaries 2 Main Results 3 Conclusion References Coupled Fixed Points for Multivalued Feng–Liu-Type Contractions with Application to Nonlinear Integral Equation 1 Introduction and Mathematical Background 2 Main Results 3 Some Consequences 4 Application to Nonlinear Integral Equations References Fractals Clifford-Valued Fractal Interpolation 1 Introduction 2 A Brief Introduction to Clifford Algebra and Analysis 3 Some Results from Fractal Interpolation Theory 4 Clifford-Valued Fractal Interpolation 5 Paravector-Valued Functions 6 Brief Summary and Further Research Directions References Optimal Quantizers for a Nonuniform Distribution on a Sierpiński Carpet 1 Introduction 2 Preliminaries 3 Optimal Sets of n-means for All n2 4 Some Results and Observations References Fractal Dimension for a Class of Complex-Valued Fractal Interpolation Functions 1 Introduction 1.1 Preliminaries 1.2 Fractal Interpolation Functions 1.3 α-Fractal Functions 2 Main Theorems References A Note on Complex-Valued Fractal Functions on the Sierpiński Gasket 1 Introduction 2 Technical Introduction 3 Fractal Interpolation Function on SG 4 Some Results Associated with the Fractal Operator 5 Conclusion References Dimensional Analysis of Mixed Riemann–Liouville Fractional Integral of Vector-Valued Functions 1 Introduction 1.1 Motivation 1.2 Delineation 2 Notations and Prelude 2.1 Fractal Dimension 2.2 Variation of a Function 2.3 Fractal Dimension and Bounded Variation 2.4 Mixed Riemann–Liouville Fractional Integral 3 Few Fundamental Concepts on Dimension of the Graph of a Vector-Valued Function 4 Riemann–Liouville Fractional Integral and Fractal Dimension 5 Conclusion and Future Scope References Fractional Operator Associated with the Fractal Integral of A-Fractal Function 1 Introduction and Preliminaries 2 Fractal Interpolation Function 2.1 Hidden Variable A-Fractal Function 3 Fractal Integral on A-Fractal Function 4 Fractional Operator References Mathematical Modeling A Multi-strain Model for COVID-19 1 Introduction 2 Single-Strain Model 2.1 Controlled Reproduction Number 3 Two-Strain Model 3.1 Effective Reproduction Number 3.2 Multi-strain Model 3.3 Numerical Example 4 Model Validation with COVID-19 Data 5 Discussion References Effect of Nonlinear Prey Refuge on Predator–Prey Dynamics 1 Introduction 2 Mathematical Model Formulation with Constant Refuge 3 Mathematical Model Formulation with Nonlinear Refuge 4 Model Comparison 5 Discussion and Conclusion References Effects of Magnetic Field and Thermal Conductivity Variance on Thermal Excitation Developed by Laser Pulses and Thermal Shock 1 Introduction 2 Laser Pulse Heat Source 3 Basic Equations Using Dual-Phase Lag Thermoelasticity 4 Mathematical Modelling of the Problem 5 Initial and Boundary Conditions 6 Solution in Laplace Transform Domain 7 Quantitative Results 7.1 Effects of Magnetic Field 7.2 Effects of Changing Thermal Conductivity 8 Conclusion References Differential and Integral Equations On Unique Positive Solution of Hadamard Fractional Differential Equation Involving p-Laplacian 1 Introduction 2 Preliminaries 3 Existence and Uniqueness 4 Conclusion References Eigenvalue Criteria for Existence and Nonexistence of Positive Solutions for α-Order Fractional Differential Equations on the Half-Line (2