Solution of Fractional Differential Equation of Variable Order via S-Iteration

The present chapter studies the solvability of the initial value problem for the variable-order fractional differential equation (FDE) involving the Caputo fractional derivative in Banach space. The existence and uniqueness of the solution of FDE is studied using the application of the S-iteration method. Since the study of qualitative properties usually requires the use of differential and integral inequalities, the S-iteration method contributes equally to the study of various properties such as dependence on initial data, the closeness of solutions, and dependence on parameters and functions involved in the right side of the FDE. Finally, we illustrate our main result through an example.