Existence and stability of a nonlinear fractional differential equation involving a $\psi$-Caputo operator

Authors : Hanan A WAHASH, Mohammed ABDO, Satish K PANCHAL

Pages : 266-278

Doi:10.31197/atnaa.664534

View : 11 | Download : 6

Publication Date : 2020-12-30

Article Type : Research Paper

Abstract :This paper is devoted to the study of the existence and interval of existence, uniqueness of solutions and estimates on solutions of the nonlocal Cauchy problem for nonlinear fractional differential equations involving a Caputo type fractional derivative with respect to another function $\psi$. Further, we prove four different types of Ulam stability results of solutions for a given problem. The tools used in this article are the classical technique of Banach fixed point theorem and generalized Gronwall inequality. At the end, illustrative examples are presented.
Keywords : fractional differential equations, Existence and stability, Fixed point theorem, ψ fractional derivative and ψ fractional integral