Existence, uniqueness, continuous dependence and Ulam stability of mild solutions for an iterative fractional differential equation

Abstract

In this work, we study the existence, uniqueness, continuous dependence and Ulam stability of mild solutions for an iterative Caputo fractional differential equation by first inverting it as an integral equation. Then we construct an appropriate mapping and employ the Schauder fixed point theorem to prove our new results. At the end we give an example to illustrate our obtained results. RESUMENEn este trabajo, estudiamos la existencia, unicidad, dependencia continua y estabilidad de Ulam de soluciones mild para una ecuación diferencial fraccionaria de Caputo iterativa, invirtiéndola primero como ecuación integral. Luego construimos una aplicación apropiada y empleamos el teorema del punto fijo de Schauder para demostrar nuestros nuevos resultados. Finalmente damos un ejemplo para ilustrar los resultados obtenidos.

On Solutions to Fractional Iterative Differential Equations with Caputo Derivative

“…Because of the applicability of integer and fractional derivative in modeling, many articles that deal about the ordinary and fractional iterative diferential equation have been investigated. We may refer the reader directly to the papers [5][6][7][8] for ordinary derivative and [9][10][11][12] for fractional derivative. Tere are various defnitions for fractional integral and derivatives.…”