Approximate controllability of semilinear non-autonomous evolution systems with state-dependent delay

Existence and approximate controllability of Hilfer fractional evolution equations with almost sectorial operators

“…Under some admissible control inputs, exact controllability steers the system to arbitrary final state, while approximate controllability steers the system to the small neighborhood of arbitrary final state. In the published works, there are numerous articles focussing on the exact or approximate controllability of systems represented by FDEs, neutral FDEs, FDEs with impulsive inclusions, and FDEs with delay functions [4,18,40,44].…”

Approximate controllability of a non-autonomous evolution equation in Banach spaces

“…Approximate controllability of non-autonomous semilinear systems in Hilbert spaces with various conditions can be obtained from [21,23], etc. Fu in [20] investigated the approximate controllability of semilinear non-autonomous evolution systems in Hilbert spaces with state-dependent delay. Using the resolvent operators, the approximate controllability results for fractional differential equations in Hilbert spaces is explored by Fan in [17].…”

Non-autonomous stochastic evolution equations with nonlinear noise and nonlocal conditions governed by noncompact evolution families

“…We notice that among the previous researches, most of researchers focus on the case that the differential operators in the main parts are independent of time t, which means that the problems under consideration are autonomous. However, when treating some parabolic evolution equations, it is usually assumed that the partial differential operators depend on time t on account of this class of operators appears frequently in the applications, for the details please see [1], [2], [3], [10], [11], [12], [20], [24] and [30]. Therefore, it is interesting and significant to investigate stochastic non-autonomous evolution equations with nonlocal initial conditions, i.e., the differential operators in the main parts of the considered problems are dependent of time t. Motivated by the above mentioned aspects, in this paper, we will investigate the existence of mild solutions for the non-autonomous stochastic evolution equations of parabolic type with nonlocal initial conditions (1).…”

“…We point out that the work of this paper is the following two wedges: on the one hand, to the best of the author's knowledge, all the existing articles used various methods to study autonomous stochastic evolution equations, i.e., the differential operators in the main parts of the considered problems are independent of time t, but for the case that the corresponding differential operators in the main parts are dependent of time t, we have not seen the relevant papers to study non-autonomous stochastic evolution equations with nonlocal initial conditions. In order to fill this gap, we are concerned with the existence of mild solutions for NSEE (1) in this paper; on the other hand, we notice that non-autonomous evolution equations have been extensively studied in recent years using various fixed point theorems when the corresponding evolution family is compact, see for example [3,20,24,30], this is very convenient to the equations with compact resolvent. But for the case that the corresponding evolution family is noncompact, we have not seen the relevant papers to study non-autonomous stochastic evolution equations of parabolic type with nonlocal initial conditions.…”