Generalized Darbo-Type F -Contraction and F -Expansion and Its Applications to a Nonlinear Fractional-Order Differential Equation

Abstract

In this work, we introduce various Darbo-type F£-contractions, and utilizing these contractions, we present some fixed point theorems. Moreover, we introduce a Darbo-type F£-expanding mapping and prove fixed point theorems under the Darbo-type F£-expanding mapping. Employing our results, we check the existence of a solution to the nonlinear fractional-order differential equation under the integral type boundary conditions. For its validity, an appropriate example is given. © 2020 Mian Bahadur Zada et al.