The technique of Volterra–Stieltjes integral equations in the application to infinite systems of nonlinear integral equations of fractional orders

Abstract

Our study in this paper concerns the infinite systems of nonlinear integral equations of Volterra–Stieltjes type. We show that some assumptions imposed on terms of the mentioned systems guarantee the solvability of those systems in the space C(I,c0) with I=[0,1] and c0 being the classical sequence space. As a particular and very important case of the investigated systems of nonlinear Volterra–Stieltjes integral equations we obtain infinite systems of nonlinear integral equations of fractional orders. Thus, the approach applied in the paper enables us to obtain rather general results concerning the existence of solutions of infinite systems of nonlinear fractional integral equations.