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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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
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spelling doaj-f5d2698f97d54d6d89d4b7ba8b831b592020-11-25T03:30:30ZengMDPI AGComputation2079-31972020-05-018494910.3390/computation8020049A New Generalized Definition of Fractional Derivative with Non-Singular KernelKhalid Hattaf0Centre Régional des Métiers de l’Education et de la Formation (CRMEF), Derb Ghalef 20340, Casablanca, MoroccoThis 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.https://www.mdpi.com/2079-3197/8/2/49fractional derivativenon-singular kernelMittag–Lefler functionfractional differential equationsepidemiology
collection DOAJ
language English
format Article
sources DOAJ
author Khalid Hattaf
spellingShingle Khalid Hattaf
A New Generalized Definition of Fractional Derivative with Non-Singular Kernel
Computation
fractional derivative
non-singular kernel
Mittag–Lefler function
fractional differential equations
epidemiology
author_facet Khalid Hattaf
author_sort Khalid Hattaf
title A New Generalized Definition of Fractional Derivative with Non-Singular Kernel
title_short A New Generalized Definition of Fractional Derivative with Non-Singular Kernel
title_full A New Generalized Definition of Fractional Derivative with Non-Singular Kernel
title_fullStr A New Generalized Definition of Fractional Derivative with Non-Singular Kernel
title_full_unstemmed A New Generalized Definition of Fractional Derivative with Non-Singular Kernel
title_sort new generalized definition of fractional derivative with non-singular kernel
publisher MDPI AG
series Computation
issn 2079-3197
publishDate 2020-05-01
description 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.
topic fractional derivative
non-singular kernel
Mittag–Lefler function
fractional differential equations
epidemiology
url https://www.mdpi.com/2079-3197/8/2/49
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