{"product_id":"computational-fractional-dynamical-systems-isbn-9781119696957","title":"Computational Fractional Dynamical Systems","description":"\u003cb\u003eComputational Fractional Dynamical Systems\u003c\/b\u003e \u003cp\u003e\u003cb\u003eA rigorous presentation of different expansion and semi-analytical methods for fractional differential equations\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003eFractional differential equations, differential and integral operators with non-integral powers, are used in various science and engineering applications. Over the past several decades, the popularity of the fractional derivative has increased significantly in diverse areas such as electromagnetics, financial mathematics, image processing, and materials science. Obtaining analytical and numerical solutions of nonlinear partial differential equations of fractional order can be challenging and involve the development and use of different methods of solution. \u003c\/p\u003e\u003cp\u003e\u003ci\u003eComputational Fractional Dynamical Systems: Fractional Differential Equations and Applications \u003c\/i\u003epresents a variety of computationally efficient semi-analytical and expansion methods to solve different types of fractional models. Rather than focusing on a single computational method, this comprehensive volume brings together more than 25 methods for solving an array of fractional-order models. The authors employ a rigorous and systematic approach for addressing various physical problems in science and engineering.  \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003e Covers various aspects of efficient methods regarding fractional-order systems\u003c\/li\u003e \u003cli\u003e Presents different numerical methods with detailed steps to handle basic and advanced equations in science and engineering\u003c\/li\u003e \u003cli\u003e Provides a systematic approach for handling fractional-order models arising in science and engineering \u003c\/li\u003e \u003cli\u003eIncorporates a wide range of methods with corresponding results and validation\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003e\u003ci\u003eComputational Fractional Dynamical Systems: Fractional Differential Equations and Applications\u003c\/i\u003e is an invaluable resource for advanced undergraduate students, graduate students, postdoctoral researchers, university faculty, and other researchers and practitioners working with fractional and integer order differential equations. \u003c\/p\u003e\u003cp\u003ePreface\u003c\/p\u003e \u003cp\u003eAcknowledgments\u003c\/p\u003e \u003cp\u003eAbout the Authors\u003c\/p\u003e \u003cp\u003e                Introduction to Fractional Calculus\u003c\/p\u003e \u003cp\u003e1.1.          Introduction\u003c\/p\u003e \u003cp\u003e1.2.          Birth of fractional calculus\u003c\/p\u003e \u003cp\u003e1.3.          Useful mathematical functions\u003c\/p\u003e \u003cp\u003e      1.3.1.       The gamma function\u003c\/p\u003e \u003cp\u003e      1.3.2.       The beta function\u003c\/p\u003e \u003cp\u003e      1.3.3.       The Mittag-Leffler function     \u003c\/p\u003e \u003cp\u003e      1.3.4.       The Mellin-Ross function\u003c\/p\u003e \u003cp\u003e      1.3.5.       The Wright function\u003c\/p\u003e \u003cp\u003e      1.3.6.       The error function\u003c\/p\u003e \u003cp\u003e      1.3.7.       The hypergeometric function\u003c\/p\u003e \u003cp\u003e1.3.8.       The H-function\u003c\/p\u003e \u003cp\u003e1.4.          Riemann–Liouville fractional integral and derivative\u003c\/p\u003e \u003cp\u003e1.5.          Caputo fractional derivative\u003c\/p\u003e \u003cp\u003e1.6.          Grünwald-Letnikov fractional derivative and integral\u003c\/p\u003e \u003cp\u003e1.7.          Riesz fractional derivative and integral\u003c\/p\u003e \u003cp\u003e1.8.          Modified Riemann-Liouville derivative\u003c\/p\u003e \u003cp\u003e      1.9.          Local fractional derivative\u003c\/p\u003e \u003cp\u003e1.9.1.       Local fractional continuity of a function\u003c\/p\u003e \u003cp\u003e1.9.2.       Local fractional derivative\u003c\/p\u003e \u003cp\u003e                References\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e                Recent Trends in Fractional Dynamical Models and Mathematical Methods\u003c\/p\u003e \u003cp\u003e2.1.          Introduction\u003c\/p\u003e \u003cp\u003e2.2.          Fractional calculus: A generalization of integer-order calculus\u003c\/p\u003e \u003cp\u003e2.3.          Fractional derivatives of some functions and their graphical illustrations\u003c\/p\u003e \u003cp\u003e2.4.          Applications of fractional calculus\u003c\/p\u003e \u003cp\u003e2.4.1.       N.H. Abel and Tautochronous problem\u003c\/p\u003e \u003cp\u003e2.4.2.       Ultrasonic wave propagation in human cancellous bone\u003c\/p\u003e \u003cp\u003e2.4.3.       Modeling of speech signals using fractional calculus\u003c\/p\u003e \u003cp\u003e2.4.4.       Modeling the cardiac tissue electrode interface using fractional calculus\u003c\/p\u003e \u003cp\u003e2.4.5.     Application of fractional calculus to the sound waves propagation in rigid porous                      Materials\u003c\/p\u003e \u003cp\u003e2.4.6.        Fractional calculus for lateral and longitudinal control of autonomous vehicles\u003c\/p\u003e \u003cp\u003e2.4.7.        Application of fractional calculus in the theory of viscoelasticity\u003c\/p\u003e \u003cp\u003e2.4.8.        Fractional differentiation for edge detection\u003c\/p\u003e \u003cp\u003e2.4.9.        Wave propagation in viscoelastic horns using a fractional calculus rheology model\u003c\/p\u003e \u003cp\u003e2.4.10.      Application of fractional calculus to fluid mechanics\u003c\/p\u003e \u003cp\u003e2.4.11.      Radioactivity, exponential decay and population growth\u003c\/p\u003e \u003cp\u003e2.4.12.      The Harmonic oscillator\u003c\/p\u003e \u003cp\u003e2.5.           Overview of some analytical\/numerical methods\u003c\/p\u003e \u003cp\u003e2.5.1.        Fractional Adams–Bashforth\/Moulton methods\u003c\/p\u003e \u003cp\u003e2.5.2.        Fractional Euler method\u003c\/p\u003e \u003cp\u003e2.5.3.          Finite difference method\u003c\/p\u003e \u003cp\u003e2.5.4.          Finite element method\u003c\/p\u003e \u003cp\u003e2.5.5.        Finite volume method\u003c\/p\u003e \u003cp\u003e2.5.6.        Meshless method\u003c\/p\u003e \u003cp\u003e2.5.7.        Reproducing kernel Hilbert space method\u003c\/p\u003e \u003cp\u003e2.5.8.        Wavelet method\u003c\/p\u003e \u003cp\u003e2.5.9.        The Sine-Gordon expansion method\u003c\/p\u003e \u003cp\u003e2.5.10.      The Jacobi elliptic equation method\u003c\/p\u003e \u003cp\u003e2.5.11.      The generalized Kudryashov method\u003c\/p\u003e \u003cp\u003e                 References\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e                Adomian Decomposition Method (ADM)\u003c\/p\u003e \u003cp\u003e3.1.           Introduction\u003c\/p\u003e \u003cp\u003e3.2.           Basic Idea of  ADM\u003c\/p\u003e \u003cp\u003e3.3.           Numerical Examples\u003c\/p\u003e \u003cp\u003e                 References\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e                Adomian Decomposition Transform Method\u003c\/p\u003e \u003cp\u003e4.1.            Introduction\u003c\/p\u003e \u003cp\u003e4.2.            Transform methods for the Caputo sense derivatives\u003c\/p\u003e \u003cp\u003e4.3.            Adomian decomposition Laplace transform method (ADLTM)\u003c\/p\u003e \u003cp\u003e4.4.            Adomian decomposition Sumudu transform method (ADSTM)\u003c\/p\u003e \u003cp\u003e4.5.            Adomian decomposition Elzaki transform method (ADETM)\u003c\/p\u003e \u003cp\u003e4.6.            Adomian decomposition Aboodh transform method (ADATM)\u003c\/p\u003e \u003cp\u003e4.7.            Numerical Examples\u003c\/p\u003e \u003cp\u003e4.7.1.         Implementation of ADLTM\u003c\/p\u003e \u003cp\u003e4.7.2.         Implementation of ADSTM\u003c\/p\u003e \u003cp\u003e4.7.3.         Implementation of ADETM\u003c\/p\u003e \u003cp\u003e4.7.4.         Implementation of ADATM\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e                   References\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e                Homotopy Perturbation Method (HPM)\u003c\/p\u003e \u003cp\u003e5.1.            Introduction\u003c\/p\u003e \u003cp\u003e5.2.            Procedure of HPM\u003c\/p\u003e \u003cp\u003e5.3.            Numerical examples\u003c\/p\u003e \u003cp\u003e                  References\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e                Homotopy Perturbation Transform Method\u003c\/p\u003e \u003cp\u003e6.1.            Introduction\u003c\/p\u003e \u003cp\u003e6.2.            Transform methods for the Caputo sense derivatives\u003c\/p\u003e \u003cp\u003e6.3.            Homotopy perturbation Laplace transform method (HPLTM)\u003c\/p\u003e \u003cp\u003e6.4.            Homotopy perturbation Sumudu transform method (HPSTM)\u003c\/p\u003e \u003cp\u003e6.5.            Homotopy perturbation Elzaki transform method (HPETM)\u003c\/p\u003e \u003cp\u003e6.6.            Homotopy perturbation Aboodh transform method (HPATM)\u003c\/p\u003e \u003cp\u003e6.7.            Numerical Examples\u003c\/p\u003e \u003cp\u003e6.7.1.         Implementation of HPLTM\u003c\/p\u003e \u003cp\u003e6.7.2.         Implementation of HPSTM\u003c\/p\u003e \u003cp\u003e6.7.3.         Implementation of HPETM\u003c\/p\u003e \u003cp\u003e6.7.4.         Implementation of HPATM\u003c\/p\u003e \u003cp\u003e                  References\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e                Fractional Differential Transform Method\u003c\/p\u003e \u003cp\u003e7.1.            Introduction\u003c\/p\u003e \u003cp\u003e7.2.            Fractional differential transform method\u003c\/p\u003e \u003cp\u003e7.3.            Illustrative Examples\u003c\/p\u003e \u003cp\u003e                  References\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e                Fractional Reduced Differential Transform Method\u003c\/p\u003e \u003cp\u003e8.1.            Introduction\u003c\/p\u003e \u003cp\u003e8.2.            Description of FRDTM\u003c\/p\u003e \u003cp\u003e8.3.            Numerical Examples\u003c\/p\u003e \u003cp\u003e                  References\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e                Variational Iterative Method\u003c\/p\u003e \u003cp\u003e9.1.            Introduction\u003c\/p\u003e \u003cp\u003e9.2.            Procedure for VIM\u003c\/p\u003e \u003cp\u003e9.3.            Examples\u003c\/p\u003e \u003cp\u003e                  References\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e                 Method of Weighted Residuals\u003c\/p\u003e \u003cp\u003e 10.1.         Introduction\u003c\/p\u003e \u003cp\u003e       10.2.         Collocation method\u003c\/p\u003e \u003cp\u003e       10.3.         Least-square method\u003c\/p\u003e \u003cp\u003e       10.4.         Galerkin method\u003c\/p\u003e \u003cp\u003e       10.5.         Numerical Examples\u003c\/p\u003e \u003cp\u003e                  References\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e                 Boundary Characteristics Orthogonal Polynomials\u003c\/p\u003e \u003cp\u003e 11.1.         Introduction\u003c\/p\u003e \u003cp\u003e 11.2.         Gram–Schmidt orthogonalization procedure\u003c\/p\u003e \u003cp\u003e 11.3.         Generation of BCOPs\u003c\/p\u003e \u003cp\u003e 11.4.         Galerkin method with BCOPs\u003c\/p\u003e \u003cp\u003e 11.5.         Least-Square method with BCOPs\u003c\/p\u003e \u003cp\u003e 11.6.         Application Problems\u003c\/p\u003e \u003cp\u003e                  References\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e                 Residual Power Series Method\u003c\/p\u003e \u003cp\u003e12.1.           Introduction\u003c\/p\u003e \u003cp\u003e12.2.           Theorems and lemma related to RPSM\u003c\/p\u003e \u003cp\u003e12.3.           Basic idea of RPSM\u003c\/p\u003e \u003cp\u003e12.4.           Convergence Analysis\u003c\/p\u003e \u003cp\u003e12.5.           Examples\u003c\/p\u003e \u003cp\u003e                   References\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e                Homotopy Analysis Method\u003c\/p\u003e \u003cp\u003e13.1.           Introduction\u003c\/p\u003e \u003cp\u003e13.2.           Theory of homotopy analysis method\u003c\/p\u003e \u003cp\u003e13.3.           Convergence theorem of HAM\u003c\/p\u003e \u003cp\u003e13.4.           Test Examples\u003c\/p\u003e \u003cp\u003e                   References\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e                Homotopy Analysis Transform Method\u003c\/p\u003e \u003cp\u003e14.1.           Introduction\u003c\/p\u003e \u003cp\u003e      14.2.           Transform methods for the Caputo sense derivative\u003c\/p\u003e \u003cp\u003e      14.3.           Homotopy analysis Laplace transform method (HALTM)\u003c\/p\u003e \u003cp\u003e      14.4.           Homotopy analysis Sumudu transform method (HASTM)\u003c\/p\u003e \u003cp\u003e      14.5.           Homotopy analysis Elzaki transform method (HAETM)\u003c\/p\u003e \u003cp\u003e      14.6.           Homotopy analysis Aboodh transform method (HAATM)\u003c\/p\u003e \u003cp\u003e      14.7.           Numerical Examples\u003c\/p\u003e \u003cp\u003e      14.7.1.         Implementation of HALTM\u003c\/p\u003e \u003cp\u003e      14.7.2.         Implementation of HASTM\u003c\/p\u003e \u003cp\u003e      14.7.3.         Implementation of HAETM\u003c\/p\u003e \u003cp\u003e      14.7.4.         Implementation of HAATM\u003c\/p\u003e \u003cp\u003e                         References\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e                 q-Homotopy Analysis Method\u003c\/p\u003e \u003cp\u003e 15.1.         Introduction\u003c\/p\u003e \u003cp\u003e 15.2.         Theory of q-HAM\u003c\/p\u003e \u003cp\u003e 15.3.         Illustrative Examples\u003c\/p\u003e \u003cp\u003e                  References\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e                  q-Homotopy Analysis transform Method\u003c\/p\u003e \u003cp\u003e  16.1.         Introduction\u003c\/p\u003e \u003cp\u003e  16.2.         Transform methods for the Caputo sense derivative\u003c\/p\u003e \u003cp\u003e        16.3.         q-homotopy analysis Laplace transform method (q-HALTM)\u003c\/p\u003e \u003cp\u003e        16.4.         q-homotopy analysis Sumudu transform method (q-HASTM)\u003c\/p\u003e \u003cp\u003e        16.5.         q-homotopy analysis Elzaki transform method (q-HAETM)\u003c\/p\u003e \u003cp\u003e        16.6.         q-homotopy analysis Aboodh transform method (q-HAATM)\u003c\/p\u003e \u003cp\u003e        16.7.         Test Problems\u003c\/p\u003e \u003cp\u003e        16.7.1.        Implementation of q-HALTM\u003c\/p\u003e \u003cp\u003e        16.7.2.        Implementation of q-HASTM\u003c\/p\u003e \u003cp\u003e        16.7.3.        Implementation of q-HAETM\u003c\/p\u003e \u003cp\u003e        16.7.4.        Implementation of q-HAATM\u003c\/p\u003e \u003cp\u003e                          References\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e                  (G'\/G)-Expansion Method\u003c\/p\u003e \u003cp\u003e   17.1.          Introduction\u003c\/p\u003e \u003cp\u003e   17.2.          Description of the (G'\/G)-expansion method\u003c\/p\u003e \u003cp\u003e   17.3.          Application Problems\u003c\/p\u003e \u003cp\u003e                     References\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e                  (G’\/G^2)-Expansion Method\u003c\/p\u003e \u003cp\u003e   18.1.          Introduction\u003c\/p\u003e \u003cp\u003e 18.2.            Description of the (G’\/G^2)-expansion method\u003c\/p\u003e \u003cp\u003e 18.3.            Numerical Examples\u003c\/p\u003e \u003cp\u003e                     References\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e                  (G’\/G,1\/G)-Expansion Method\u003c\/p\u003e \u003cp\u003e  19.1.           Introduction\u003c\/p\u003e \u003cp\u003e  19.2.           Algorithm of the (G’\/G,1\/G)-expansion method\u003c\/p\u003e \u003cp\u003e  19.3.           Illustrative Examples\u003c\/p\u003e \u003cp\u003e                     References\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e                 The modified simple equation method\u003c\/p\u003e \u003cp\u003e 20.1.           Introduction\u003c\/p\u003e \u003cp\u003e 20.2.           Procedure of the modified simple equation method\u003c\/p\u003e \u003cp\u003e 20.3.           Application Problems\u003c\/p\u003e \u003cp\u003e                    References\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e                 Sine-Cosine Method\u003c\/p\u003e \u003cp\u003e 21.1.           Introduction\u003c\/p\u003e \u003cp\u003e 21.2.           Details of Sine-Cosine method\u003c\/p\u003e \u003cp\u003e 21.3.           Numerical Examples\u003c\/p\u003e \u003cp\u003e                    References\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e                 Tanh Method\u003c\/p\u003e \u003cp\u003e 22.1.            Introduction\u003c\/p\u003e \u003cp\u003e 22.2.            Description of the Tanh method\u003c\/p\u003e \u003cp\u003e 22.3.            Numerical Examples\u003c\/p\u003e \u003cp\u003e                     References\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e                 Fractional sub-equation method\u003c\/p\u003e \u003cp\u003e 23.1.            Introduction\u003c\/p\u003e \u003cp\u003e 23.2.            Implementation of the fractional sub-equation method\u003c\/p\u003e \u003cp\u003e 23.3.            Numerical Examples\u003c\/p\u003e \u003cp\u003e                     References\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e                 Exp-function Method\u003c\/p\u003e \u003cp\u003e 24.1.           Introduction\u003c\/p\u003e \u003cp\u003e 24.2.           Procedure of the Exp-function method\u003c\/p\u003e \u003cp\u003e 24.3.           Numerical Examples\u003c\/p\u003e \u003cp\u003e                    References\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e                 Exp(-φ(ξ))-expansion method\u003c\/p\u003e \u003cp\u003e 25.1.          Introduction\u003c\/p\u003e \u003cp\u003e 25.2.          Methodology of the exp(-φ(ξ))-expansion method\u003c\/p\u003e \u003cp\u003e 25.3.          Numerical Examples\u003c\/p\u003e \u003cp\u003e                   References\u003c\/p\u003e \u003cp\u003eIndex\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eSnehashish Chakraverty,\u003c\/b\u003e Senior Professor, Department of Mathematics (Applied Mathematics Group), National Institute of Technology Rourkela, Odisha, India.  \u003c\/p\u003e\u003cp\u003e\u003cb\u003eRajarama Mohan Jena,\u003c\/b\u003e Senior Research Fellow, Department of Mathematics, National Institute of Technology Rourkela, Odisha, India.  \u003c\/p\u003e\u003cp\u003e\u003cb\u003eSubrat Kumar Jena,\u003c\/b\u003e Senior Research Fellow, Department of Mathematics, National Institute of Technology Rourkela, Odisha, India.   \u003c\/p\u003e\u003cp\u003e\u003cb\u003eA rigorous presentation of different expansion and semi-analytical methods for fractional differential equations\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003eFractional differential equations, differential and integral operators with non-integral powers, are used in various science and engineering applications. Over the past several decades, the popularity of the fractional derivative has increased significantly in diverse areas such as electromagnetics, financial mathematics, image processing, and materials science. Obtaining analytical and numerical solutions of nonlinear partial differential equations of fractional order can be challenging and involve the development and use of different methods of solution. \u003c\/p\u003e\u003cp\u003e\u003ci\u003eComputational Fractional Dynamical Systems: Fractional Differential Equations and Applications \u003c\/i\u003epresents a variety of computationally efficient semi-analytical and expansion methods to solve different types of fractional models. Rather than focusing on a single computational method, this comprehensive volume brings together more than 25 methods for solving an array of fractional-order models. The authors employ a rigorous and systematic approach for addressing various physical problems in science and engineering.  \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003e Covers various aspects of efficient methods regarding fractional-order systems\u003c\/li\u003e \u003cli\u003e Presents different numerical methods with detailed steps to handle basic and advanced equations in science and engineering\u003c\/li\u003e \u003cli\u003e Provides a systematic approach for handling fractional-order models arising in science and engineering \u003c\/li\u003e \u003cli\u003eIncorporates a wide range of methods with corresponding results and validation\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003e\u003ci\u003eComputational Fractional Dynamical Systems: Fractional Differential Equations and Applications\u003c\/i\u003e is an invaluable resource for advanced undergraduate students, graduate students, postdoctoral researchers, university faculty, and other researchers and practitioners working with fractional and integer order differential equations.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47988965310693,"sku":"NP9781119696957","price":130.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781119696957.jpg?v=1761782237","url":"https:\/\/k12savings.com\/products\/computational-fractional-dynamical-systems-isbn-9781119696957","provider":"K12savings","version":"1.0","type":"link"}