An Extension of the Picard Theorem to Fractional Differential Equations with a Caputo-Fabrizio Derivative - H. R. Marasi; A. Soltani Joujehi; H. Aydi (Journal of Function Spaces)
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.