Mixed fractional differential equation with nonlocal conditions in Banach spaces

Abstract

This paper is devoted to study the existence of solution for a class of  nonlinear differential equations with nonlocal boundary conditions involving the right Caputo and left Riemann--Liouville fractional derivatives. Our approach is based on Darbo's fixed point theorem associated with the Hausdorff measure of noncompactness. The obtained results generalize and extend some of the results found in the literature. Besides, the reported results concerned in the Banach space's sense. In the end,  an example illustrates our acquired results.