Please use this identifier to cite or link to this item:
http://hdl.handle.net/10773/35144
Title: | The power fractional calculus: first definitions and properties with applications to power fractional differential equations |
Author: | Lotfi, El Mehdi Zine, Houssine Torres, Delfim F. M. Yousfi, Noura |
Keywords: | Generalized Mittag–Leffler function Fractional calculus Non-singular kernels Integro-differential equations |
Issue Date: | 1-Oct-2022 |
Publisher: | MDPI |
Abstract: | Using the Laplace transform method and the convolution theorem, we introduce new and more general definitions for fractional operators with non-singular kernels, extending well-known concepts existing in the literature. The new operators are based on a generalization of the Mittag–Leffler function, characterized by the presence of a key parameter p. This power parameter p is important to enable researchers to choose an adequate notion of the derivative that properly represents the reality under study, to provide good mathematical models, and to predict future dynamic behaviors. The fundamental properties of the new operators are investigated and rigorously proved. As an application, we solve a Caputo and a Riemann–Liouville fractional differential equation. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/35144 |
DOI: | 10.3390/math10193594 |
Publisher Version: | https://www.mdpi.com/2227-7390/10/19/3594 |
Appears in Collections: | CIDMA - Artigos SCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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[520]power_fract_calc.pdf | 313.93 kB | Adobe PDF | View/Open |
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