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Trends in Mathematics

Fractional Calculus and Fractional Differential Equations

Editors: Daftardar-Gejji, Varsha (Ed.)

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  • Discusses recent developments in fractional calculus and fractional differential equations
  • Focuses on applications in pure mathematics, applied mathematics, statistics, and engineering
  • Covers topics on numerical analysis of fractional differential equations, fractional Poisson processes, fractional calculus in complex domains, variable-order fractional operators, and fractional-order delay differential equations
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eBook $89.00
price for USA in USD (gross)
  • ISBN 978-981-13-9227-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.99
price for USA in USD
  • Customers within the U.S. and Canada please contact Customer Service at +1-800-777-4643, Latin America please contact us at +1-212-460-1500 (24 hours a day, 7 days a week).
  • Due: August 10, 2019
  • ISBN 978-981-13-9226-9
  • Free shipping for individuals worldwide
About this book

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.


About the authors

Varsha Daftardar-Gejji is Professor at the Department of Mathematics, Savitribai Phule Pune University, India. She completed her Ph.D. at Pune University, India. She has developed original methods for solving fractional differential equations that have become widely popular. Her noteworthy contributions include analysis of fractional differential equations, and developing theories of fractional-ordered dynamical systems and related phenomena such as chaos. She is the editor of the book Fractional Calculus: Theory and Applications and co-authored the book Differential Equations (Schaum’s Outline Series). She has published more than 65 papers in respected international journals in areas of fractional calculus, fractional differential equations and general relativity.

Table of contents (8 chapters)

Table of contents (8 chapters)
  • Numerics of Fractional Differential Equations

    Pages 1-16

    Daftardar-Gejji, Varsha

  • Adomian Decomposition Method and Fractional Poisson Processes: A Survey

    Pages 17-39

    Kataria, K. K. (et al.)

  • On Mittag-Leffler Kernel-Dependent Fractional Operators with Variable Order

    Pages 41-58

    Bahaa, G. M. (et al.)

  • Analysis of 2-Term Fractional-Order Delay Differential Equations

    Pages 59-75

    Bhalekar, Sachin

  • Stability Analysis of Two-Dimensional Incommensurate Systems of Fractional-Order Differential Equations

    Pages 77-92

    Brandibur, Oana (et al.)

Buy this book

eBook $89.00
price for USA in USD (gross)
  • ISBN 978-981-13-9227-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.99
price for USA in USD
  • Customers within the U.S. and Canada please contact Customer Service at +1-800-777-4643, Latin America please contact us at +1-212-460-1500 (24 hours a day, 7 days a week).
  • Due: August 10, 2019
  • ISBN 978-981-13-9226-9
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Fractional Calculus and Fractional Differential Equations
Editors
  • Varsha Daftardar-Gejji
Series Title
Trends in Mathematics
Copyright
2019
Publisher
Birkhäuser Basel
Copyright Holder
Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-13-9227-6
DOI
10.1007/978-981-13-9227-6
Hardcover ISBN
978-981-13-9226-9
Series ISSN
2297-0215
Edition Number
1
Number of Pages
XI, 180
Number of Illustrations
4 b/w illustrations, 32 illustrations in colour
Topics