The Power Fractional Calculus: First Definitions and Properties with Applications to Power Fractional Differential Equations

Autor:	El Mehdi Lotfi, Houssine Zine, Delfim F. M. Torres, Noura Yousfi
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	generalized Mittag–Leffler function fractional calculus non-singular kernels integro-differential equations Mathematics QA1-939
Zdroj:	Mathematics, Vol 10, Iss 19, p 3594 (2022)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math10193594
Popis:	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.
Databáze:	Directory of Open Access Journals
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