A New Class of Generalized Fractal and Fractal-Fractional Derivatives with Non-Singular Kernels

The present paper introduces a new class of generalized differential and integral operators. This class includes and generalizes a large number of definitions of fractal-fractional derivatives and integral operators used to model the complex dynamics of many natural and physical phenomena found in d...

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Bibliographic Details
Published inFractal and fractional Vol. 7; no. 5; p. 395
Main Author Hattaf, Khalid
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.05.2023
Subjects
Chaos theory
chaotic system
Coronaviruses
COVID-19
fractal-fractional derivative
fractal-fractional integral
Fractals
Integrals
Numerical analysis
numerical scheme
Operators (mathematics)
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ISSN2504-3110
2504-3110
DOI10.3390/fractalfract7050395

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Summary:The present paper introduces a new class of generalized differential and integral operators. This class includes and generalizes a large number of definitions of fractal-fractional derivatives and integral operators used to model the complex dynamics of many natural and physical phenomena found in diverse fields of science and engineering. Some properties of the newly introduced class are rigorously established. As applications of this new class, two illustrative examples are presented, one for a simple problem and the other for a nonlinear problem modeling the dynamical behavior of a chaotic system.
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ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract7050395