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This paper is concerned with the existence of continuous solutions of a set-valued functional integral equation of Volterra–Stieltjes type. 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 to an initial-value problem of arbitrary fractional-order differential inclusion.

On the existence of solutions of a set-valued functional integral equation of Volterra–Stieltjes type and some applications