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Fractional Calculus and Fractional Differential Equations

  • Varsha Daftardar-Gejji
Conference proceedings

Part of the Trends in Mathematics book series (TM)

About these proceedings

Introduction

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.

Keywords

Adomian Decomposition Method Mittag-Leffler Kernel Fractional Order Artificial Neural Network Comparison Theorems Sumudu Transform Iterative Method

Editors and affiliations

  • Varsha Daftardar-Gejji
    • 1
  1. 1.Department of MathematicsSavitribai Phule Pune UniversityPuneIndia

Bibliographic information

  • DOI https://doi.org/10.1007/978-981-13-9227-6
  • Copyright Information Springer Nature Singapore Pte Ltd. 2019
  • Publisher Name Birkhäuser, Singapore
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-981-13-9226-9
  • Online ISBN 978-981-13-9227-6
  • Series Print ISSN 2297-0215
  • Series Online ISSN 2297-024X
  • Buy this book on publisher's site
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