Nonlocal Cauchy Problem via a Fractional Operator Involving Power Kernel in Banach Spaces

Nonlocal Cauchy Problem via a Fractional Operator Involving Power Kernel in Banach Spaces

We investigated existence and uniqueness conditions of solutions of a nonlinear differential equation containing the Caputo–Fabrizio operator in Banach spaces. The mentioned derivative has been proposed by using the exponential decay law and hence it removed the computational complexities...

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Bibliographic Details
Main Authors: Ayşegül Keten, Mehmet Yavuz, Dumitru Baleanu
Format: Article
Language:English
Published: MDPI AG 2019-05-01
Series:Fractal and Fractional
Subjects:
existence-uniqueness conditions
nonlocal Cauchy problem
Caputo–Fabrizio fractional derivative
Banach space
Online Access:https://www.mdpi.com/2504-3110/3/2/27
Description
Summary:We investigated existence and uniqueness conditions of solutions of a nonlinear differential equation containing the Caputo–Fabrizio operator in Banach spaces. The mentioned derivative has been proposed by using the exponential decay law and hence it removed the computational complexities arising from the singular kernel functions inherit in the conventional fractional derivatives. The method used in this study is based on the Banach contraction mapping principle. Moreover, we gave a numerical example which shows the applicability of the obtained results.
ISSN:2504-3110

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