Analysis on ψ-Hilfer Fractional Impulsive Differential Equations

In this manuscript, we establish the existence of results of fractional impulsive differential equations involving psi-Hilfer fractional derivative and almost sectorial operators using Schauder fixed-point theorem. We discuss two cases, if the associated semigroup is compact and noncompact, respectively. We consider here the higher-dimensional system of integral equations. We present herewith new theoretical results, structural investigations, and new models and approaches. Some special cases of the results are discussed as well. Due to the nature of measurement of noncompactness theory, there exists a strong relationship between the sectorial operator and symmetry. When working on either of the concepts, it can be applied to the other one as well. Finally, a case study is presented to demonstrate the major theory.

Automated summary

In this paper, the existence of results of fractional impulsive differential equations involving psi-Hilfer fractional derivative and almost sectorial operators is established using the Schauder fixed-point theorem. Two cases are discussed based on whether the associated semigroup is compact or noncompact. New theoretical results, structural investigations, and models/approaches are presented, with a focus on the relationship between sectorial operators and symmetry. Lastly, a case study is presented to illustrate the main theory.