Study on Sobolev type Hilfer evolution equations with non-instantaneous impulses

Abstract

In this article, we deal with the existence of mild solutions for a class of Sobolev type Hilfer fractional equation with non-instantaneous impulses in Banach spaces. By mean of an operator family generated by the operator pair $(A,B)$ and probability density function, the definition of mild solutions for studied problem was given. The main result is obtained by using the techniques of fractional calculus, measure of noncompactness and Sadovskii fixed point theorem. To the end, an example is given to illustrate the abstract results.

Keywords:

• Hilfer fractional derivative
• Hilfer evolution equations
• non-instantaneous impulses
• mild solution

2000 AMS Subject Classifications:

• 26A33
• 34K30
• 34K45
• 47G10
• 47D06

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

National Natural Science Foundation of China (Grant No. 12061062). Science Research Project for Colleges and Universities of Gansu Province (No.2022A-010).