Controllability of Neutral Impulsive Itô Type Stochastic Integrodifferential Systems

Controllability for some integrodifferential equations driven by vector measures

“…Assume that (A1)-(A2) hold. Then, there exists a unique resolvent operator of the Cauchy problem (7).…”

“…Integrodifferential equations have attracted much attention because of their applications in many areas : physics, population dynamics, electrical engineering, medicine biology, ecology, and other areas of science and engineering. Qualitative properties such as existence, uniqueness, controllability, and stability for various integrodifferential equations have been extensively studied by many researchers, refer to . The corresponding literature for the studies of integrodifferential equations of type is large too, but for control theory, to the best of our knowledge, there is no literature on the controllability with vector measures as controls.…”

Boundary controllability of nonlocal Hilfer fractional stochastic differential systems with fractional Brownian motion and Poisson jumps

“…Stochastic differential equations driven by fractional Brownian motion have been considered extensively by research community in various aspects due to the salient features for real world problems (see [5][6][7][8][9][10][11][12]). In addition, controllability problems for different kinds of dynamical systems have been studied by several authors (see [13][14][15][16][17][18][19][20][21]), and the references therein. Few authors studied the controllability for linear and nonlinear systems when the control is on the boundary (see [22][23][24][25][26][27][28][29][30]).…”

CONTROLLABILITY OF SOBOLEV TYPE NONLOCAL IMPULSIVE MIXED FUNCTIONAL INTEGRODIFFERENTIAL EVOLUTION SYSTEMS Vol. 3(1) Jan 2015, No. 11, pp. 122-132 KAMALENDRA KUMAR, RAKESH KUMAR

“…On the other hand, most of the practical systems are integrodifferential equations in nature and hence the study of integrodifferential equations is very important. Many authors studied mixed type integrodifferential systems with (or without) delay conditions [11], [23], [24], [28], [29], and [30]. Recently, Machado et al [22] establish the controllability for a class of abstract impulsive mixed type functional integrodifferential equations with finite delay in a Banach space by using the Mö nch fixed point theorem via measure of noncompactness and semigroup theory.…”

“…A Sobolev-type equation constitute an important field of research due to their numerous applications such as flow of fluids through fissured rocks, thermodynamics, shear in second order fluids and propagation of long waves of small amplitude. Many researchers [6], [8], and [30] investigated the problem of controllability of Sobolevtype integrodifferential systems in Banach space. Recently, Ahmed [1] have studied the sufficient conditions for controllability of Sobolev-type fractional integrodifferential systems in a Banach space by using the compact semigroup and Schauder fixed point theorem.…”