Monotone iterative technique for multi-term time fractional measure differential equations

Abstract

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 nonlocal conditions in an ordered Banach spaces. Firstly, we look for suitable concept of S-asymptotically \(\omega \)-periodic mild solution to our concern problem, by means of Laplace transform and \((\beta ,\gamma _k)\)-resolvent family \(\{S_{\beta ,\gamma _k}(t)\}_{t\ge 0}\). Secondly, we construct monotone iterative method in the presence of the lower and upper solutions to the delayed fractional measure differential equations, and obtain the existence of maximal and minimal S-asymptotically \(\omega \)-periodic mild solutions for the mentioned system. Finally, as the application of abstract results, an example is given to illustrate our main results.