A generalization of truncated M-fractional derivative and applications to fractional differential equations
- Autores: Esin Ilhan, I.Onur Kıymaz
- Localización: Applied Mathematics and Nonlinear Sciences, ISSN-e 2444-8656, Vol. 5, Nº. 1, 2020, págs. 171-188
- Idioma: inglés
- DOI: 10.2478/amns.2020.1.00016
- Enlaces
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Resumen
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 integerorder derivatives. Finally, we obtain the analytical solutions of some M-series fractional differential equations.
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