In the presented research, uniqueness and existence of a mild solution for fractional system semilinear evolution equations with infinite delay an infinitesimal generator operator are demonstrated. The generalized Liouville–Caputo derivative non-integer-order 1<??2 parameter 0<?<1 used to establish our model. ?-Laplace transform strongly continuous cosine sine families uniformly bounde...

Here we deal with the stabilisation problem of non-diagonal systems by boundary control. In studied setting, control input is subject to a constant delay. We use spectral decomposition method and split system into two components: an unstable stable one. To stabilise part system, connect, for first time in literature, famous backstepping design technique direct-proportional design. More precisel...

This paper is devoted to investigating one type of nonlinear two-term fractional order delayed differential equations involving Caputo derivatives. The Leray–Schauder alternative fixed-point theorem and Banach contraction principle are applied analyze the existence uniqueness solutions problem with infinite delay. Additionally, Hyers–Ulam stability considered for delay conditions.