An Extension of the Picard Theorem to Fractional Differential Equations with a Caputo-Fabrizio Derivative. (15th March 2021) - Marasi, H. R.; Joujehi, A. Soltani; Aydi, H.
Abstract : In this paper, we consider fractional differential equations with the new fractional derivative involving a nonsingular kernel, namely, the Caputo-Fabrizio fractional derivative. Using a successive approximation method, we prove an extension of the Picard-Lindelöf existence and uniqueness theorem for fractional differential equations with this derivative, which gives a set of conditions, under which a fractional initial value problem has a unique solution.