Overview
- Presents recent research and applications on generalized fractional calculus
- Applies generalized fractional differentiation techniques of Caputo, Canavati, and Conformable types to a great variety of integral inequalities, e.g., of Ostrowski and Opial types
- Lays foundations of stochastic fractional calculus
- Includes self-contained and original chapters which can be read independently
Part of the book series: Studies in Systems, Decision and Control (SSDC, volume 305)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (22 chapters)
-
Front Matter
Keywords
About this book
This book applies generalized fractional differentiation techniques of Caputo, Canavati and Conformable types to a great variety of integral inequalities e.g. of Ostrowski and Opial types, etc. Some of these are extended to Banach space valued functions. These inequalities have also great impact in numerical analysis, stochastics and fractional differential equations. The book continues with generalized fractional approximations by positive sublinear operators which derive from the presented Korovkin type inequalities and also includes abstract cases. It presents also multivariate complex Korovkin quantitative approximation theory. It follows M-fractional integral inequalities of Ostrowski and Polya types. The results are weighted so they provide a great variety of cases and applications. The second part of the book deals with the quantitative fractional Korovkin type approximation of stochastic processes and lays there the foundations of stochastic fractional calculus. The book considers both Caputo and Conformable fractional directions and derives regular and trigonometric results. The positive linear operators can be expectation operator commutative or not. This book results are expected to find applications in many areas of pure and applied mathematics and stochastics. As such this monograph is suitable for researchers, graduate students, and seminars of the above disciplines, also to be in all science and engineering libraries.
Authors and Affiliations
Bibliographic Information
Book Title: Generalized Fractional Calculus
Book Subtitle: New Advancements and Applications
Authors: George A. Anastassiou
Series Title: Studies in Systems, Decision and Control
DOI: https://doi.org/10.1007/978-3-030-56962-4
Publisher: Springer Cham
eBook Packages: Intelligent Technologies and Robotics, Intelligent Technologies and Robotics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-56961-7Published: 26 November 2020
Softcover ISBN: 978-3-030-56964-8Published: 27 November 2021
eBook ISBN: 978-3-030-56962-4Published: 25 November 2020
Series ISSN: 2198-4182
Series E-ISSN: 2198-4190
Edition Number: 1
Number of Pages: XV, 498
Number of Illustrations: 1 b/w illustrations
Topics: Control and Systems Theory, Computational Intelligence