Study of Certain Classes of ψ -Hilfer Fractional Differential Equations: Qualitative Properties and Some Applications

Abstract

The theory of fractional differential equations provides a powerful framework for modeling systems with memory and hereditary properties. The ψ-Hilfer fractional derivative serves as a unifying and flexible operator, generalizing several classical derivatives through suitable choices of the weight function y and type parameter B. This dissertation focuses on the qualitative analysis of fractional differential equations involving the ψ-Hilfer derivative, with particular emphasis on Ulam-type stability.