Approximate controllability of neutral stochastic evolution inclusions via fractional substantial derivative

K. Nandhaprasadh, R. Udhayakumar

In this study, we investigate the approximate controllability of neutral stochastic evolution inclusions with infinite delay, governed by a fractional substantial derivative. We first establish the existence of a mild solution using fractional calculus, fixed point theory, and stochastic theory. Subsequently, we prove the approximate controllability of the system under appropriate assumptions. To validate the theoretical results, a representative example is presented. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 19(1) (2026), pp. 177-198