Existence results for mixed Hadamard and Riemann-Liouville fractional integro-differential inclusions

Abstract

In this paper, we investigate a new class of mixed initial value problems of Hadamard and RiemannLiouville fractional integro-differential inclusions. The existence of solutions for convex valued (the upper semicontinuous) case is established by means of Krasnoselskii's fixed point theorem for multivalued maps and nonlinear alternative criterion, while the existence result for non-convex valued maps (the Lipschitz case) relies on a fixed point theorem due to Covitz and Nadler. Illustrative examples are also included.

On a System of Coupled Langevin Equations in the Frame of Generalized Liouville–Caputo Fractional Derivatives

“…The results were compared with those found for the same GLE. The aforementioned papers [8][9][10][11][12][13] and their relevant references contain recent findings on the LE with varied boundary conditions. In light of the numerous applications that it has in the fields of engineering, the social sciences, and the technical sciences, the study of fractional calculus has arisen as an important subject in which to do research.…”