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

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This article investigates the solvability and approximate controllability of a new class of measure driven control systems with state-dependent delay, which can deal with hybrid system without any restriction Zeno behaviour. By applying fixed point technology and Lebesgue Stieltjes integral, a new set of sufficient conditions is constructed that ensures the existence of mild solution and approximate controllability of the considered system. Lastly, an example is formulated to demonstrate the effectiveness of obtained results.