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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| Vydané v: | Applied mathematics and nonlinear sciences Ročník 5; číslo 1; s. 171 - 188 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Beirut
Sciendo
01.01.2020
De Gruyter Brill Sp. z o.o., Paradigm Publishing Services |
| Predmet: | |
| ISSN: | 2444-8656, 2444-8656 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | 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. |
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| Bibliografia: | 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 |