In this article, we establish the existence of solutions for a functional integral equation of fractional order. The study upholds the case when the set-valued function has L 1-Carathèodory selections, we reformulate the functional integral inclusion according to these selections via a classical fixed point theorem of Schauder and present theorem for the existence of integrable solutions. As an application, the existence of solutions of nonlinear functional integro-differential inclusion with an initial value, and the initial value problem for the arbitrary-order differential inclusion will be studied.
In this paper, we study the existence of continuous solutions of a set-valued functional integral equation for the Volterra-Stieltjes type. The asymptotic stability of the solutions will be studied. The continuous dependence of the solution on the set of selections of the set-valued function will be proven. As an application, we study the existence of solutions of an initial value problem of arbitrary (fractional) order differential inclusion.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.