EXISTENCE AND UNIQUENESS OF THE SOLUTION OF THE FRACTIONAL DIFFERENTIAL EQUATION VIA A NEW THREE STEPS ITERATION.

In this paper, we study the existence, uniqueness, and other properties of solution of differential equation of fractional order involving the Caputo fractional derivative. The tool employed in the analysis is based on the application of a new three steps iteration process introduced by V. Karakaya, Y. Atalan, K. Dogan, and NH. Bouzara [26]. Furthermore, the study of various properties such as dependence on initial data, the closeness of solutions, and dependence on parameters and functions involved therein. The results obtained are illustrated through an example. [ABSTRACT FROM AUTHOR]