A study on mild solutions for multi-term time fractional measure differential equations

Abstract

In this paper, we investigate the existence and uniqueness of the S-asymptotically ω-periodic mild solutions to a class of multi-term time-fractional measure differential equations with initial conditions in Banach spaces. Firstly, we look for a suitable concept of S-asymptotically ω-periodic mild solution to our concerned problem, by means of the Laplace transform and $(\beta ,{\gamma }_k)$-resolvent family $\{S_{\beta ,{\gamma }_k}(t){\}}_{t\ge 0}$. Secondly, the existence of S-asymptotically ω-periodic mild solutions for the mentioned system is obtained by utilizing regulated functions and fixed point theorem. Finally, as the application of abstract results, an example is given to illustrate our main results.

Keywords:

• Regulated functions
• Henstock–Lebesgue–Stieltjes integral
• measure differential equations
• S-asymptotically ω-periodic

2000 AMS Subject Classifications:

• 26A33
• 34G20
• 34K37
• 39A99
• 46G99

Acknowledgments

This work is supported by National Natural Science Foundation of China (11661071, 12061062) and Science Research Project for Colleges and Universities of Gansu Province (No. 2022A-010) and Project of NWNU-LKQN2023-02.

Disclosure statement

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

Additional information

Funding

This work was supported by National Natural Science Foundation of China[12061062].