Extension of Chaplygin's existence and uniqueness method for fractal-fractional nonlinear differential equations

The existence and uniqueness of solutions to nonlinear ordinary differential equations with fractal-fractional derivatives, with Dirac-delta, exponential decay, power law, and generalized Mittag-Leffler kernels, have been the focus of this work. To do this, we used the Chaplygin approach, which enta...

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Bibliographic Details
Published inAIMS mathematics Vol. 9; no. 3; pp. 5763 - 5793
Main Authors Atangana, Abdon, Araz, Seda İğret
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2024
Subjects
chaplygin's method
existence and uniqueness
fractal-fractional differentiation and integration
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Summary:The existence and uniqueness of solutions to nonlinear ordinary differential equations with fractal-fractional derivatives, with Dirac-delta, exponential decay, power law, and generalized Mittag-Leffler kernels, have been the focus of this work. To do this, we used the Chaplygin approach, which entails creating two lower and upper sequences that converge to the solution of the equations under consideration. We have for each case provided the conditions under which these sequences are obtained and converge.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2024280