Exploring Variable Order Fractional Initial Value Problems: Existence Results and Weak Topology Insights

Abstract

The aim of this paper is to fill an absence in the study of initial value problems with weak topology that use variable order fractional calculus. Using Krasnoselskii’s type fixed point theorem under weak topology, we construct suitable conditions to assure the existence of weak solutions for various types of initial value problems involving variable order Riemann-Liouville fractional derivative. Some examples are provided to illustrate the results.