Advances in Fuzzy Integral and Differential Equations: 412 (Studies in Fuzziness and Soft Computing, 412)

Description

As the title of the book suggests, the topics of this book are organized into two parts. The first part points out the fuzzy differential equations and the second one is related to the fuzzy integral equations. The book contains nine chapters that six chapters are about fuzzy differential equations and three of them are about fuzzy integral equations. In each part, the chapters’ authors are going to discuss the topics theoretically and numerically. All researchers and students in the field of mathematical, computer, and also engineering sciences can benefit from the subjects of the book. Contents Fuzzy Differential Equations Differential and Integral Calculus for Fuzzy Number-Valued Functions with Interactivity 1 Introduction 2 Mathematical Background 3 Interactive Fuzzy Numbers 4 Differential Calculus for mathcalF-Interactive Fuzzy Processes 5 A-Linearly Interactive Fuzzy Processes 5.1 Differential and Integral Calculus for A-Linearly Interactive Fuzzy Processes 5.2 Fuzzy Differential Equations for A-Linearly Interactive Processes 5.3 The Fuzzy Laplace Transform for A-Linearly Interactive Process 5.4 Linear Fuzzy Partial Differential Equation in mathbbRF(A) References The Transform Method to Solve Fuzzy Differential Equation via Differential Inclusions 1 Introduction 2 The Method 2.1 The Transform Method 3 Mathieu System with Fuzzy Uncertainties 4 Rotor/stator Rubbing System with Fuzzy Uncertainties 5 Conclusion References Complete Controllability of Fuzzy Fractional Evolutions Equation Under Fréchet Derivative in Linear Correlated Fuzzy Spaces 1 Introduction 2 Preliminaries 2.1 The Space of Linear Correlated Fuzzy Numbers 2.2 Laplace Transformation for Functions in mathbbRmathcalF(A) 2.3 The C0—Semigroup of Fuzzy-Valued Mappings 2.4 Measure of Noncompactness and Condensing Mappings 3 Complete Controllability 4 Conclusions References An Estimation of the Solution of First Order Fuzzy Differential Equations 1 Introduction 2 Preliminaries 3 Numerical Methods 3.1 Modified Euler Method 3.2 Piecewise Approximation Method 4 Numerical Example References Solution Strategy for Fuzzy Fractional Order Linear Homogeneous Differential Equation by Caputo-H Differentiability and Its Application in Fuzzy EOQ Model 1 Introduction 2 Preliminaries 3 Fractional Homogeneous Linear Differential Equations of Order α 3.1 Case-1 3.2 Case-2 4 Application: EOQ Model with Stock Depended Demand 4.1 Mathematical Modelling 4.2 Numerical Illustration 4.3 Graphical Analysis 5 Conclusion References Homotopy Perturbation Method for Solving Fuzzy Fractional Heat-Conduction Equation 1 Introduction 2 Preliminaries 2.1 Fuzzy Number 2.2 Triangular Fuzzy Number (TFN) 2.3 Double Parametric Form (DPF) of Fuzzy Number 3 Double Parametric Form of Fuzzy Fractional Heat Equation 4 Homotopy Perturbation Method for the Solution of FFHE 4.1 Numerical Implementation of the Proposed Method 5 Conclusion References Fuzzy Integral Equations Finding Optimal Results in the Homotopy Analysis Method to Solve Fuzzy Integral Equations 1 Introduction 2 Fuzzy CESTAC Method 3 Main Idea 4 Numerical Examples 5 Conclusion References Numerical Solution of Some Singular Volterra Fuzzy Integral Equations of the First Kind by Fuzzy Generalized Quadrature Formula 1 Introduction 2 Preliminaries 3 Introduce the FGQF 4 Error Estimation 4.1 Fuzzy Taylor Formula 4.2 Error Bound 5 Numerical Examples References Successive Approximations Method for Fuzzy Fredholm-Volterra Integral equations of the Second Kind 1 Introduction 2 Preliminaries 3 Quadrature Formulas 4 Two Dimensional Fuzzy Integral Equations 5 The Successive Approximations Method 6 Error Analysis 7 Numerical Examples 8 Conclusion References