On Katugampola Fractional Operator and Katugampola Pantograph Problems in Jα,β

Source abstract

This paper explores and establishes solvability results for a nonlinear Katugampola fractional pantograph initial value problem formulated in the integral‐type Hölder space . The constructed model blends generalized fractional dynamics with proportional delay terms, offering a unified setting for studying systems with memory‐dependent behavior. To obtain the principal results, we begin by establishing several analytical properties of Katugampola‐type fractional operators on , such as continuity, boundedness, and their mapping behavior. These properties are subsequently combined with fixed‐point techniques and the Hausdorff measure of noncompactness to establish existence and uniqueness of solutions under appropriate hypotheses. The theoretical findings are further illustrated through two representative examples and a numerical experiment for various choices of α and β , thereby confirming the practical relevance of the proposed framework.