Taylor’s Formula for Generalized Weighted Fractional Derivatives with Nonsingular Kernels
Houssine Zine,
El Mehdi Lotfi,
Delfim F. M. Torres,
Noura Yousfi
Affiliations
Houssine Zine
Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
El Mehdi Lotfi
Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M’sik, Hassan II University of Casablanca, P.O. Box 7955, Sidi Othman, Casablanca 20000, Morocco
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, P.O. Box 7955, Sidi Othman, Casablanca 20000, Morocco
We prove a new Taylor’s theorem for generalized weighted fractional calculus with nonsingular kernels. The proof is based on the establishment of new relations for nth-weighted generalized fractional integrals and derivatives. As an application, new mean value theorems for generalized weighted fractional operators are obtained. Direct corollaries allow one to obtain the recent Taylor’s and mean value theorems for Caputo–Fabrizio, Atangana–Baleanu–Caputo (ABC) and weighted ABC derivatives.
