By choosing appropriate norms, a fractional integral operator can be taken as a contraction mapping on the Dimovski spaces which lie between the spaces of continuous and integrable functions on a compact interval. This fact can be used to prove existence-uniqueness results for many fractional differential equations, and also to construct explicit solutions in the form of locally uniformly convergent series. Detailed proofs are given here for Riemann–Liouville integrals, but the same methodology can and should be used for many other fractional integral operators.
Arran Fernandez (Wed,) studied this question.