A generalization of truncated M-fractional derivative and applications to fractional differential equations

In this paper, our aim is to generalize the truncated M-fractional derivative which was recently introduced [Sousa and de Oliveira, A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties, Inter. of Jour. Analy. and Appl., 16 (1), 83–96, 2018]...

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Veröffentlicht in:Applied mathematics and nonlinear sciences Jg. 5; H. 1; S. 171 - 188
Hauptverfasser: İlhan, Esin, Kıymaz, İ. Onur
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Beirut Sciendo 01.01.2020
De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
Schlagworte:
26A33
33E20
34A08
alternative fractional derivative
conformable fractional derivative
M-series
Truncated M-fractional derivative
ISSN:2444-8656, 2444-8656
Online-Zugang:Volltext
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Zusammenfassung:In this paper, our aim is to generalize the truncated M-fractional derivative which was recently introduced [Sousa and de Oliveira, A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties, Inter. of Jour. Analy. and Appl., 16 (1), 83–96, 2018]. To do that, we used generalized M-series, which has a more general form than Mittag-Leffler and hypergeometric functions. We called this generalization as truncated ℳ-series fractional derivative. This new derivative generalizes several fractional derivatives and satisfies important properties of the integer-order derivatives. Finally, we obtain the analytical solutions of some ℳ-series fractional differential equations.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2444-8656
2444-8656
DOI:10.2478/amns.2020.1.00016