TOPOLOGICAL STRUCTURE OF SOLUTION SET FOR \(\psi\)-HILFER FRACTIONAL DIFFERENTIAL EQUATIONS IN BANACH SPACE

In this paper, we investigate the topological structure of the solution set for the initial value problem associated with \(\psi\) $\psi$ -Hilfer fractional differential equations in Banach space. We show that the solution set of the fractional Cauchy problem is nonempty, compact, and an \(R_{\delta }\) $R_{\delta }$ -set. This result allows to apply a fixed result for condensing maps in the weighted space of continuous functions. Finally, an example to illustrate the applications of the main result is also given.