Computational fractional dynamical systems : fractional differential equations and applications

Computational fractional dynamical systems fractional differential equations and applications

Bibliographic Details
Other Authors: Jena, Rajarama Mohan, author (author), Jena, Subrat Kumar, author
Format: eBook
Language:Inglés
Published: Hoboken, N.J.: Wiley 2023.
Hoboken, New Jersey : [2023]
Subjects:
Fractional differential equations.
Differential equations.
Integral operators.
See on Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009811330406719
Table of Contents:
  • Cover
  • Title Page
  • Copyright Page
  • Contents
  • Preface
  • Acknowledgments
  • About the Authors
  • Chapter 1 Introduction to Fractional Calculus
  • 1.1 Introduction
  • 1.2 Birth of Fractional Calculus
  • 1.3 Useful Mathematical Functions
  • 1.3.1 The Gamma Function
  • 1.3.2 The Beta Function
  • 1.3.3 The Mittag-Leffler Function
  • 1.3.4 The Mellin-Ross Function
  • 1.3.5 The Wright Function
  • 1.3.6 The Error Function
  • 1.3.7 The Hypergeometric Function
  • 1.3.8 The H-Function
  • 1.4 Riemann-Liouville (R-L) Fractional Integral and Derivative
  • 1.5 Caputo Fractional Derivative
  • 1.6 Grünwald-Letnikov Fractional Derivative and Integral
  • 1.7 Riesz Fractional Derivative and Integral
  • 1.8 Modified Riemann-Liouville Derivative
  • 1.9 Local Fractional Derivative
  • 1.9.1 Local Fractional Continuity of a Function
  • 1.9.2 Local Fractional Derivative
  • References
  • Chapter 2 Recent Trends in Fractional Dynamical Models and Mathematical Methods
  • 2.1 Introduction
  • 2.2 Fractional Calculus: A Generalization of Integer-Order Calculus
  • 2.3 Fractional Derivatives of Some Functions and Their Graphical Illustrations
  • 2.4 Applications of Fractional Calculus
  • 2.4.1 N.H. Abel and Tautochronous problem
  • 2.4.2 Ultrasonic Wave Propagation in Human Cancellous Bone
  • 2.4.3 Modeling of Speech Signals Using Fractional Calculus
  • 2.4.4 Modeling the Cardiac Tissue Electrode Interface Using Fractional Calculus
  • 2.4.5 Application of Fractional Calculus to the Sound Waves Propagation in Rigid Porous Materials
  • 2.4.6 Fractional Calculus for Lateral and Longitudinal Control of Autonomous Vehicles
  • 2.4.7 Application of Fractional Calculus in the Theory of Viscoelasticity
  • 2.4.8 Fractional Differentiation for Edge Detection
  • 2.4.9 Wave Propagation in Viscoelastic Horns Using a Fractional Calculus Rheology Model.
  • 2.4.10 Application of Fractional Calculus to Fluid Mechanics
  • 2.4.11 Radioactivity, Exponential Decay, and Population Growth
  • 2.4.12 The Harmonic Oscillator
  • 2.5 Overview of Some Analytical/Numerical Methods
  • 2.5.1 Fractional Adams-Bashforth/Moulton Methods
  • 2.5.2 Fractional Euler Method
  • 2.5.3 Finite Difference Method
  • 2.5.4 Finite Element Method
  • 2.5.5 Finite Volume Method
  • 2.5.6 Meshless Method
  • 2.5.7 Reproducing Kernel Hilbert Space Method
  • 2.5.8 Wavelet Method
  • 2.5.9 The Sine-Gordon Expansion Method
  • 2.5.10 The Jacobi Elliptic Equation Method
  • 2.5.11 The Generalized Kudryashov Method
  • References
  • Chapter 3 Adomian Decomposition Method
  • 3.1 Introduction
  • 3.2 Basic Idea of ADM
  • 3.3 Numerical Examples
  • References
  • Chapter 4 Adomian Decomposition Transform Method
  • 4.1 Introduction
  • 4.2 Transform Methods for the Caputo Sense Derivatives
  • 4.3 Adomian Decomposition Laplace Transform Method (ADLTM)
  • 4.4 Adomian Decomposition Sumudu Transform Method (ADSTM)
  • 4.5 Adomian Decomposition Elzaki Transform Method (ADETM)
  • 4.6 Adomian Decomposition Aboodh Transform Method (ADATM)
  • 4.7 Numerical Examples
  • 4.7.1 Implementation of ADLTM
  • 4.7.2 Implementation of ADSTM
  • 4.7.3 Implementation of ADETM
  • 4.7.4 Implementation of ADATM
  • References
  • Chapter 5 Homotopy Perturbation Method
  • 5.1 Introduction
  • 5.2 Procedure for HPM
  • 5.3 Numerical Examples
  • References
  • Chapter 6 Homotopy Perturbation Transform Method
  • 6.1 Introduction
  • 6.2 Transform Methods for the Caputo Sense Derivatives
  • 6.3 Homotopy Perturbation Laplace Transform Method (HPLTM)
  • 6.4 Homotopy Perturbation Sumudu Transform Method (HPSTM)
  • 6.5 Homotopy Perturbation Elzaki Transform Method (HPETM)
  • 6.6 Homotopy Perturbation Aboodh Transform Method (HPATM)
  • 6.7 Numerical Examples
  • 6.7.1 Implementation of HPLTM.
  • 6.7.2 Implementation of HPSTM
  • 6.7.3 Implementation of HPETM
  • 6.7.4 Implementation of HPATM
  • References
  • Chapter 7 Fractional Differential Transform Method
  • 7.1 Introduction
  • 7.2 Fractional Differential Transform Method
  • 7.3 Illustrative Examples
  • References
  • Chapter 8 Fractional Reduced Differential Transform Method
  • 8.1 Introduction
  • 8.2 Description of FRDTM
  • 8.3 Numerical Examples
  • References
  • Chapter 9 Variational Iterative Method
  • 9.1 Introduction
  • 9.2 Procedure for VIM
  • 9.3 Examples
  • References
  • Chapter 10 Weighted Residual Methods
  • 10.1 Introduction
  • 10.2 Collocation Method
  • 10.3 Least-Square Method
  • 10.4 Galerkin Method
  • 10.5 Numerical Examples
  • References
  • Chapter 11 Boundary Characteristic Orthogonal Polynomials
  • 11.1 Introduction
  • 11.2 Gram-Schmidt Orthogonalization Procedure
  • 11.3 Generation of BCOPs
  • 11.4 Galerkin Method with BCOPs
  • 11.5 Least-Square Method with BCOPs
  • 11.6 Application Problems
  • References
  • Chapter 12 Residual Power Series Method
  • 12.1 Introduction
  • 12.2 Theorems and Lemma Related to RPSM
  • 12.3 Basic Idea of RPSM
  • 12.4 Convergence Analysis
  • 12.5 Examples
  • References
  • Chapter 13 Homotopy Analysis Method
  • 13.1 Introduction
  • 13.2 Theory of Homotopy Analysis Method
  • 13.3 Convergence Theorem of HAM
  • 13.4 Test Examples
  • References
  • Chapter 14 Homotopy Analysis Transform Method
  • 14.1 Introduction
  • 14.2 Transform Methods for the Caputo Sense Derivative
  • 14.3 Homotopy Analysis Laplace Transform Method (HALTM)
  • 14.4 Homotopy Analysis Sumudu Transform Method (HASTM)
  • 14.5 Homotopy Analysis Elzaki Transform Method (HAETM)
  • 14.6 Homotopy Analysis Aboodh Transform Method (HAATM)
  • 14.7 Numerical Examples
  • 14.7.1 Implementation of HALTM
  • 14.7.2 Implementation of HASTM
  • 14.7.3 Implementation of HAETM.
  • 14.7.4 Implementation of HAATM
  • References
  • Chapter 15 q-Homotopy Analysis Method
  • 15.1 Introduction
  • 15.2 Theory of q-HAM
  • 15.3 Illustrative Examples
  • References
  • Chapter 16 q-Homotopy Analysis Transform Method
  • 16.1 Introduction
  • 16.2 Transform Methods for the Caputo Sense Derivative
  • 16.3 q-Homotopy Analysis Laplace Transform Method (q-HALTM)
  • 16.4 q-Homotopy Analysis Sumudu Transform Method (q-HASTM)
  • 16.5 q-Homotopy Analysis Elzaki Transform Method (q-HAETM)
  • 16.6 q-Homotopy Analysis Aboodh Transform Method (q-HAATM)
  • 16.7 Test Problems
  • 16.7.1 Implementation of q-HALTM
  • 16.7.2 Implementation of q-HASTM
  • 16.7.3 Implementation of q-HAETM
  • 16.7.4 Implementation of q-HAATM
  • References
  • Chapter 17 (G/G)-Expansion Method
  • 17.1 Introduction
  • 17.2 Description of the (G/G)-Expansion Method
  • 17.3 Application Problems
  • References
  • Chapter 18 (G/G2)-Expansion Method
  • 18.1 Introduction
  • 18.2 Description of the (G/G2)-Expansion Method
  • 18.3 Numerical Examples
  • References
  • Chapter 19 (G/G, 1/G)-Expansion Method
  • 19.1 Introduction
  • 19.2 Algorithm of the (G/G,1/G)-Expansion Method
  • 19.3 Illustrative Examples
  • References
  • Chapter 20 The Modified Simple Equation Method
  • 20.1 Introduction
  • 20.2 Procedure of the Modified Simple Equation Method
  • 20.3 Application Problems
  • References
  • Chapter 21 Sine-Cosine Method
  • 21.1 Introduction
  • 21.2 Details of the Sine-Cosine Method
  • 21.3 Numerical Examples
  • References
  • Chapter 22 Tanh Method
  • 22.1 Introduction
  • 22.2 Description of the Tanh Method
  • 22.3 Numerical Examples
  • References
  • Chapter 23 Fractional Subequation Method
  • 23.1 Introduction
  • 23.2 Implementation of the Fractional Subequation Method
  • 23.3 Numerical Examples
  • References
  • Chapter 24 Exp-Function Method
  • 24.1 Introduction.
  • 24.2 Procedure of the Exp-Function Method
  • 24.3 Numerical Examples
  • References
  • Chapter 25 Exp(−φ(ξ))-Expansion Method
  • 25.1 Introduction
  • 25.2 Methodology of the Exp(−φ(ξ))-Expansion Method
  • 25.3 Numerical Examples
  • References
  • Index
  • EULA.

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