(untitled) (European Journal of Pure and Applied Mathematics, 2026)
In this article, the research examines whether Riemann-Liouville-type fractional derivatives can be used to solve an initial value problem under weak topology conditions. As a way to prove the existence of integrable description and a new type of iteration of a Leray–Schauder nonlinear alternative for the weak topology, it will be demonstrated, and the given problem is ﬁrst transformed into the sum of two integral operators, and then the modiﬁed version of Krasnoselskii’s ﬁxed point hypothesis in weak topology is employed. Finally, an example is given to illustrate the eﬀectiveness of our main ﬁndings.