Overview
- Presents numerical methods for solving partial differential and integral equations, as well as ordinary differential and integral equations
- Discusses Caputo–Fabrizio differential and integral operators, Riemann–Liouville fractional operators, and the Atangana–Baleanu fractional operators
- Helps in solving problems arising in many fields of science, technology, and engineering, such as epidemiology, chaos, solitons, fractals, diffusion, groundwater, and fluid mechanics
Part of the book series: Springer Series in Computational Mathematics (SSCM, volume 54)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (8 chapters)
-
Front Matter
Keywords
About this book
This book discusses numerical methods for solving partial differential and integral equations, as well as ordinary differential and integral equations, involving fractional differential and integral operators. Differential and integral operators presented in the book include those with exponential decay law, known as Caputo–Fabrizio differential and integral operators, those with power law, known as Riemann–Liouville fractional operators, and those for the generalized Mittag–Leffler function, known as the Atangana–Baleanu fractional operators.
The book reviews existing numerical schemes associated with fractional operators including those with power law, while also highlighting new trends in numerical schemes for recently introduced differential and integral operators. In addition, the initial chapters address useful properties of each differential and integral fractional operator. Methods discussed in the book are subsequently used to solved problems arising in many fields of science, technology, and engineering, including epidemiology, chaos, solitons, fractals, diffusion, groundwater, and fluid mechanics. Given its scope, the book offers a valuable resource for graduate students of mathematics and engineering, and researchers in virtually all fields of science, technology, and engineering, as well as an excellent addition to libraries.
Authors and Affiliations
About the authors
The main objective of his work is to use mathematical theories and methodologies to gain insights into the qualitative behavior of non-linear dynamical systems arising from the mathematical modelingof natural phenomena in the applied sciences and engineering, with an emphasis on the transmission and control dynamics of human diseases of public health interest, as well as addressing mathematical models arising in population biology for ecological patterns and processes.
ABDON ATANGANA is Full Professor at the Faculty of Natural and Agricultural Science, Institute for Groundwater Studies, University of the Free State (UFS), Bloemfontein, South Africa. He obtained his honors and master’s degrees in Applied Mathematics from the Department of Applied Mathematics at the UFS with distinction. He serves as a reviewer for more than 200 accredited international journals, and has been awarded the world champion of peer review in 2016 and in 2017. He also serves on the editorial boards of more than 20 journals of international repute. Professor Atangana’s research interests are in the methods and applications of partial and ordinary differential equations, fractional differential equations, perturbation methods, asymptotic methods, iterative methods, and groundwater modeling. He is the founder of fractional calculus with non-local and non-singular kernels, popular in applied mathematics today. Since 2013, he has published over 225 research articles in several accredited journals of applied mathematics, applied physics, geohydrology, and biomathematics. He is the author of two books, Fractional Operators with Constant and Variable Order with Application to Geo-hydrology; and Derivative with a New Parameter: Theory, Methods and Applications.
Bibliographic Information
Book Title: Numerical Methods for Fractional Differentiation
Authors: Kolade M. Owolabi, Abdon Atangana
Series Title: Springer Series in Computational Mathematics
DOI: https://doi.org/10.1007/978-981-15-0098-5
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Singapore Pte Ltd. 2019
Hardcover ISBN: 978-981-15-0097-8Published: 24 October 2019
Softcover ISBN: 978-981-15-0100-5Published: 24 October 2020
eBook ISBN: 978-981-15-0098-5Published: 14 October 2019
Series ISSN: 0179-3632
Series E-ISSN: 2198-3712
Edition Number: 1
Number of Pages: XVI, 328
Number of Illustrations: 17 b/w illustrations, 137 illustrations in colour
Topics: Partial Differential Equations, Ordinary Differential Equations, Numerical Analysis, Epidemiology