# APPROXIMATE CONTROLLABILITY OF IMPULSIVE STOCHASTIC FRACTIONAL DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

 Title APPROXIMATE CONTROLLABILITY OF IMPULSIVE STOCHASTIC FRACTIONAL DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS Publication Type Journal Article Year of Publication 2018 Authors CHADHA ALKA, BORA S.N., SAKTHIVEL R. Journal Dynamic Systems and Applications Volume 27 Issue 1 Start Page 1 Pagination 30 Date Published 01/2017 ISSN 1056-2176 AMS Subject Classification 34K30, 34K37, 35R11, 47N20, 60H15 Abstract This paper studies the approximate controllability of an impulsive neutral stochastic integro-differential equation with nonlocal conditions and infinite delay involving the Caputo fractional derivative of order $q\in(1,2)$ in separable Hilbert space. The existence of the mild solution to fractional stochastic system with nonlocal and impulsive conditions is first proved utilizing fixed point theorem, stochastic analysis, fractional calculus and solution operator theory. Then, a new set of sufficient conditions proving approximate controllability of nonlocal semilinear fractional stochastic system involving impulsive effects is derived by assuming the associated linear system is approximately controllable. Illustrating the obtained abstract results, an example is considered at the end of the paper. PDF https://acadsol.eu/dsa/articles/27/1/1.pdf DOI 10.12732/dsa.v27i1.1 Refereed Designation Refereed