Multivalued Problems, Orthogonal Mappings, and Fractional Integro-Differential Equation

Abstract

In this manuscript, we propose some sufficient conditions for the existence of solution for the multivalued orthogonal $\mathrm{ℱ}$ -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.