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Weak solutions of fractional order differential equations via Volterra-Stieltjes integral operator

El-Sayed A. M. A., El-Sayed W. G., Abd El-Mowla A. A. H.

Journal of Mathematics and Applications

2017

Vol. 40

85--96

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.