Multivalued problems via orthogonal contraction mappings with application to fractional differential equation

Abstract

In this manuscript, we give a partial answer to Reich’s problem on multivalued contraction mappings and generalize Mizoguchi–Takahashi’s fixed point theorem using a new approach of multivalued orthogonal $$(\tau ,F)$$ -contraction mappings in the framework of orthogonal metric spaces. We give a nontrivial example to prove the validity of our results. Some interesting consequences are also deduced. Finally, as application, we prove the existence and uniqueness of the solution of a nonlinear fractional differential equation.