On approximate controllability of multi-term time fractional measure differential equations with nonlocal conditions

Abstract

The purpose of this paper is to investigate the existence of mild solutions and approximate controllability of a class of multi-term time-fractional measure differential equations of hyperbolic type involving nonlocal conditions in Hilbert spaces. The approximate controllability is demonstrated by utilizing fundamental tools, namely: $$(\beta ,\gamma _{k})$$ -resolvent family, measure functional (Henstock-Lebesgue-Stieltjes integral), regulated functions and fixed point techniques. Finally, an example is presented.