A study on mild solutions for multi-term time fractional measure differential equations. (English) Zbl 07727813
Summary: In this paper, we investigate the existence and uniqueness of the \(S\)-asymptotically \(\omega\)-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 \(\omega\)-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 \(\omega\)-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.
MSC:
| 34G20 | Nonlinear differential equations in abstract spaces |
| 34A06 | Generalized ordinary differential equations (measure-differential equations, set-valued differential equations, etc.) |
| 34A08 | Fractional ordinary differential equations |
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
| 34C25 | Periodic solutions to ordinary differential equations |
Keywords:
regulated functions; Henstock-Lebesgue-Stieltjes integral; measure differential equations; \(S\)-asymptotically \(\omega\)-periodicReferences:
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