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

El Mehdi Lotfi, Houssine Zine, Delfim F. M. Torres () and Noura Yousfi
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El Mehdi Lotfi: Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M’sik, Hassan II University of Casablanca, Sidi Othman, Casablanca P.O. Box 7955, Morocco
Houssine Zine: Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
Delfim F. M. Torres: Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
Noura Yousfi: Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M’sik, Hassan II University of Casablanca, Sidi Othman, Casablanca P.O. Box 7955, Morocco

Mathematics, 2022, vol. 10, issue 19, 1-10

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.

Keywords: generalized Mittag–Leffler function; fractional calculus; non-singular kernels; integro-differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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