Nonlinear Sequential Caputo and Caputo-Hadamard Fractional Differential Equations with Dirichlet Boundary Conditions in Banach Spaces

Abstract

This paper is devoted to the existence of solutions for certain classes of nonlinear sequential Caputo and Caputo-Hadamard fractional differential equations with Dirichlet boundary conditions in Banach spaces. Moreover, our analysis is based on Darbo’s fixed point theorem in conjunction with the technique of Hausdorff measure of noncompactness. An example is also presented to illustrate the effectiveness of the main results.