Multivalued problems, orthogonal mappings, and fractional integro-differential equation (Q2225557)

Summary: In this manuscript, we propose some sufficient conditions for the existence of solution for the multivalued orthogonal \(\mathcal{F}\)-contraction mappings in the framework of orthogonal metric spaces. As a consequence of results, we obtain some interesting results. Also as application of the results obtained, we investigate Ulam's stability of fixed point problem and present a solution for the Caputo-type nonlinear fractional integro-differential equation. An example is also provided to illustrate the usability of the obtained results.