<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

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

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

In this paper, our aim is to generalize the truncated M-fractional derivative which was recently introduced [Sousa and de Oliveira, A new truncated...

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

Publié en ligne: 31 mars 2020

Pages: 171 - 188

Reçu: 25 avr. 2019

Accepté: 23 mai 2019

DOI: https://doi.org/10.2478/amns.2020.1.00016

Mots clés
Truncated M-fractional derivative, alternative fractional derivative, conformable fractional derivative, M-series

© 2020 Esin İlhan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

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

Publié en ligne: 31 mars 2020

Pages: 171 - 188

Reçu: 25 avr. 2019

Accepté: 23 mai 2019

DOI: https://doi.org/10.2478/amns.2020.1.00016

Mots clésTruncated M-fractional derivative, alternative fractional derivative, conformable fractional derivative, M-series

© 2020 Esin İlhan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Fig. 2

Fig. 3

Mots clés
Truncated M-fractional derivative, alternative fractional derivative, conformable fractional derivative, M-series