A New Generalized Definition of Fractional Derivative with Non-Singular Kernel

A New Generalized Definition of Fractional Derivative with Non-Singular Kernel

This paper proposes a new definition of fractional derivative with non-singular kernel in the sense of Caputo which generalizes various forms existing in the literature. Furthermore, the version in the sense of Riemann–Liouville is defined. Moreover, fundamental properties of the new generalized fra...

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Bibliographic Details
Main Author: Khalid Hattaf
Format: Article
Language:English
Published: MDPI AG 2020-05-01
Series:Computation
Subjects:
fractional derivative
non-singular kernel
Mittag–Lefler function
fractional differential equations
epidemiology
Online Access:https://www.mdpi.com/2079-3197/8/2/49
Description
Summary:This paper proposes a new definition of fractional derivative with non-singular kernel in the sense of Caputo which generalizes various forms existing in the literature. Furthermore, the version in the sense of Riemann–Liouville is defined. Moreover, fundamental properties of the new generalized fractional derivatives in the sense of Caputo and Riemann–Liouville are rigorously studied. Finally, an application in epidemiology as well as in virology is presented.
ISSN:2079-3197

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