Analysis of Cauchy problem with fractal-fractional differential operators

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Abstract: Cauchy problems with fractal-fractional differential operators with a power law, exponential decay, and the generalized Mittag-Leffler kernels are considered in this work. We start with deriving some important inequalities, and then by using the linear growth and Lipchitz conditions, we derive the conditions under which these equations admit unique solutions. A numerical scheme was suggested for each case to derive a numerical solution to the equation. Some examples of fractal-fractional differential equations were presented, and their exact solutions were obtained and compared with the used numerical scheme. A nonlinear case was considered and solved, and numerical solutions were presented graphically for different values of fractional orders and fractal dimensions.

Standort: Deutsche Nationalbibliothek Frankfurt am Main

Umfang: Online-Ressource

Sprache: Englisch

Erschienen in: Analysis of Cauchy problem with fractal-fractional differential operators ; volume:56 ; number:1 ; year:2023 ; extent:15
Demonstratio mathematica ; 56, Heft 1 (2023) (gesamt 15)

Urheber: Alharthi, Nadiyah Hussain
Atangana, Abdon
Alkahtani, Badr S.

DOI: 10.1515/dema-2022-0181

URN: urn:nbn:de:101:1-2023022413103370808968

Rechteinformation: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.

Letzte Aktualisierung: 14.08.2025, 10:54 MESZ

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Beteiligte

Alharthi, Nadiyah Hussain
Atangana, Abdon
Alkahtani, Badr S.

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Analysis of Cauchy problem with fractal-fractional differential operators

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