Approximate controllability of nonautonomous second-order nonlocal measure driven systems with state-dependent delay

Approximate controllability of time‐varying measure differential problem of second order with state‐dependent delay and noninstantaneous impulses

“…Therefore, our developments evolve accessorily more advanced than those existing in the publications. • The outcomes of this paper generalize the existing results in the literature for time-varying differential systems of second order and MDEs [23]. • An example is also constructed to demonstrate our findings.…”

“…Analogously, to negotiate with MDEs involving NIIs, the space of piecewise regulated functions is mandated. The integral of the map $$$ \aleph $$$ is assumed in the Bochner–Stieltjes sense. Therefore, our developments evolve accessorily more advanced than those existing in the publications. The outcomes of this paper generalize the existing results in the literature for time‐varying differential systems of second order and MDEs [23]. An example is also constructed to demonstrate our findings.…”

“…The approximate controllability is also justified under some simple sufficient conditions. The developments of this article generalize the existing outcomes in the literature for time-varying differential systems governed by second order and MDEs [23]. In the future, it is attractive to expand the works of this paper for MDEs with different fractional derivatives.…”

“…Gou and Li [22] established sufficient conditions for approximate controllability of MDEs with nonlocal conditions. Kumar and Abdal [23] examined approximate controllability for nonautonomous second-order MDEs involving state-dependent delay (SDD) and nonlocal conditions. Recently, Kumar [24] established some simple sufficient conditions for the existence of a mild solution and approximate controllability of nonautonomous MDEs with NIIs.…”

Approximate controllability of time varying measure differential problem of second order with state-dependent delay and non-instantaneous impulse

“…Recently, Gou and Li 22 established sufficient conditions for approximate controllability of MDEs with nonlocal conditions. Kumar and Abdal 23 examined approximate controllability for non-autonomous second order MDEs involving SDD and nonlocal conditions. In practice, it is worthwhile to include SDD because the modeling of physical marvels may rely on the previous states (see 24,25,26,27 ).…”