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2019 | OriginalPaper | Chapter

Reproducing Kernel Method for Fractional Derivative with Non-local and Non-singular Kernel

Author : Ali Akgül

Published in: Fractional Derivatives with Mittag-Leffler Kernel

Publisher: Springer International Publishing

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Abstract

Atangana and Baleanu introduced a derivative with fractional order to answer some outstanding questions that were posed by many investigators within the field of fractional calculus. Their derivative has a non-singular and nonlocal kernel. Therefore, we apply the reproducing kernel method to fractional differential equations with non-local and non-singular kernel. In this work, a new method has been developed for the newly established fractional differentiation. Examples are given to illustrate the numerical effectiveness of the reproducing kernel method when properly applied in the reproducing kernel space. The comparison of approximate and exact solutions leaves no doubt believing that the reproducing kernel method is very efficient and converges toward exact solution very rapidly.

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next chapter Necessary and Sufficient Optimality Conditions for Fractional Problems Involving Atangana–Baleanu’s Derivatives
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Metadata
Title
Reproducing Kernel Method for Fractional Derivative with Non-local and Non-singular Kernel
Author
Ali Akgül
Copyright Year
2019
Book
Fractional Derivatives with Mittag-Leffler Kernel

Print ISBN: 978-3-030-11661-3

Electronic ISBN: 978-3-030-11662-0

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-11662-0_1