The power fractional calculus: first definitions and properties with applications to power fractional differential equations

• Autor(a) principal: Lotfi, El Mehdi
• Data de Publicação: 2022
• Outros Autores: Zine, Houssine, Torres, Delfim F. M., Yousfi, Noura
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10773/35144
• topic: Generalized Mittag–Leffler function; Fractional calculus; Non-singular kernels; Integro-differential equations

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.