ENGLISH

Fractional Calculus and Fractional Differential Equations

By Daftardar-Gejji , Varsha (Ed.)

Book information

Publisher
Springer International Publishing
Year
2019
ISBN
978-981-13-9226-9
Language
english
Format
PDF
Filesize
6 MB (6000203 bytes)
Series
Trends in Mathematics
Edition
1
Pages
0\187
Time added
2019-08-19 04:07:05

Description

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 Front Matter ....Pages i-xi Numerics of Fractional Differential Equations (Varsha Daftardar-Gejji)....Pages 1-16 Adomian Decomposition Method and Fractional Poisson Processes: A Survey (K. K. Kataria, P. Vellaisamy)....Pages 17-39 On Mittag-Leffler Kernel-Dependent Fractional Operators with Variable Order (G. M. Bahaa, T. Abdeljawad, F. Jarad)....Pages 41-58 Analysis of 2-Term Fractional-Order Delay Differential Equations (Sachin Bhalekar)....Pages 59-75 Stability Analysis of Two-Dimensional Incommensurate Systems of Fractional-Order Differential Equations (Oana Brandibur, Eva Kaslik)....Pages 77-92 Artificial Neural Network Approximation of Fractional-Order Derivative Operators: Analysis and DSP Implementation (Pratik Kadam, Gaurav Datkhile, Vishwesh A. Vyawahare)....Pages 93-126 Theory of Fractional Differential Equations Using Inequalities and Comparison Theorems: A Survey (J. V. Devi, F. A. McRae, Z. Drici)....Pages 127-155 Exact Solutions of Fractional Partial Differential Equations by Sumudu Transform Iterative Method (Manoj Kumar, Varsha Daftardar-Gejji)....Pages 157-180

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