Weak Solutions of Fractional Order Differential Equations via Volterra-Stieltjes Integral Operator

Abstract

The fractional derivative of the Riemann-Liouville and Caputo types played an important role in the development of the theory of fractional derivatives, integrals and for its applications in pure mathematics ([18], [21]). In this paper, we study the existence of weak solutions for fractional differential equations of Riemann-Liouville and Caputo types. We depend on converting of the mentioned equations to the form of functional integral equations of Volterra-Stieltjes type in reflexive Banach spaces. AMS Subject Classification: 35D30, 34A08, 26A42.