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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Bibliographic Details
Published in:	Applied mathematics and nonlinear sciences Vol. 5; no. 1; pp. 171 - 188
Main Authors:	İlhan, Esin, Kıymaz, İ. Onur
Format:	Journal Article
Language:	English
Published:	Beirut Sciendo 01.01.2020 De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
Subjects:	26A33 33E20 34A08 alternative fractional derivative conformable fractional derivative M-series Truncated M-fractional derivative
ISSN:	2444-8656, 2444-8656
Online Access:	Get full text
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Summary:	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.
Bibliography:	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