Fractional Calculus and Fractional Differential Equations [electronic resource] /
Daftardar-Gejji, Varsha.editor.
This book provides a broad overview of the latest developments in fractional calculus and fractional differential equations (FDEs) with an aim to motivate the readers to venture into these areas. It also presents original research describing the fractional operators of variable order, fractional-order delay differential equations, chaos and related phenomena in detail. Selected results on the stability of solutions of nonlinear dynamical systems of the non-commensurate fractional order have also been included. Furthermore, artificial neural network and fractional differential equations are elaborated on; and new transform methods (for example, Sumudu methods) and how they can be employed to solve fractional partial differential equations are discussed. The book covers the latest research on a variety of topics, including: comparison of various numerical methods for solving FDEs, the Adomian decomposition method and its applications to fractional versions of the classical Poisson processes, variable-order fractional operators, fractional variational principles, fractional delay differential equations, fractional-order dynamical systems and stability analysis, inequalities and comparison theorems in FDEs, artificial neural network approximation for fractional operators, and new transform methods for solving partial FDEs. Given its scope and level of detail, the book will be an invaluable asset for researchers working in these areas.
Includes bibliographical references.
Chapter 1. Numerics of Fractional Differential Equations -- Chapter 2. Adomian Decomposition Method and Fractional Poisson Processes: A Survey -- Chapter 3. On Mittag-Leffler Kernel Dependent Fractional Operators with Variable-Order -- Chapter 4. Analysis of 2-Term Fractional Order Delay Differential Equations -- Chapter 5. Stability Analysis of Two-Dimensional Incommensurate Systems of Fractional Order Differential Equations -- Chapter 6. Artificial Neural Network Approximation of Fractional-order Derivative Operators: Analysis and DSP Implementation -- Chapter 7. Theory of Fractional Differential Equations Using Inequalities and Comparison Theorems: A Survey -- Chapter 8. Exact Solutions of Fractional Partial Differential Equations by Sumudu Transform Iterative Method.
This book provides a broad overview of the latest developments in fractional calculus and fractional differential equations (FDEs) with an aim to motivate the readers to venture into these areas. It also presents original research describing the fractional operators of variable order, fractional-order delay differential equations, chaos and related phenomena in detail. Selected results on the stability of solutions of nonlinear dynamical systems of the non-commensurate fractional order have also been included. Furthermore, artificial neural network and fractional differential equations are elaborated on; and new transform methods (for example, Sumudu methods) and how they can be employed to solve fractional partial differential equations are discussed. The book covers the latest research on a variety of topics, including: comparison of various numerical methods for solving FDEs, the Adomian decomposition method and its applications to fractional versions of the classical Poisson processes, variable-order fractional operators, fractional variational principles, fractional delay differential equations, fractional-order dynamical systems and stability analysis, inequalities and comparison theorems in FDEs, artificial neural network approximation for fractional operators, and new transform methods for solving partial FDEs. Given its scope and level of detail, the book will be an invaluable asset for researchers working in these areas.
Differential equations.
Partial differential equations.
Integral transforms.
Operational calculus.
Ordinary Differential Equations.
Partial Differential Equations.
Integral Transforms, Operational Calculus.