An extension of the Picard theorem to fractional differential equations with a Caputo-Fabrizio derivative
In this paper, fractional differential equations described by the fractional operator with exponential kernel are considered. The present operator is known as the Caputo-Fabrizio derivative. The paper addresses the problem of the existence and uniqueness of the solution of the fractional differential equation. The classical Picard-Lindelöf theorem used to prove the existence and uniqueness of differential equations with integer-order derivatives is recalled and extended in the context of fractional differential equations. One of the main novelty in this paper concerns the method used to obtain the solutions of the fractional differential equations. The recursive approximation method has been used. The procedure for obtaining the solutions of fractional differential equations recursively is illustrated via an example to support the paper's results.
scientific article; zbMATH DE number 7345479
scientific article