Computational Fractional Dynamical Systems : Fractional Differential Equations and Applications

• Autore: Jena Rajarama M
• Pubblicazione: Newark : , : John Wiley & Sons, Incorporated, , 2022; ©2023
• Descrizione fisica: 1 online resource (268 pages)
• Soggetto genere / forma: Electronic books.
• Altri autori: JenaSubrat K ChakravertySnehashish
• Nota di contenuto: 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.
• Titolo autorizzato: Computational Fractional Dynamical Systems
• ISBN: 1-119-69706-9; 1-119-69683-6
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910623984303321
• Lo trovi qui: Univ. Federico II