The Controllability of Fractional Damped Stochastic Integrodifferential Systems

Abstract

In this paper, the complete controllability is investigated for nonlinear fractional damped stochastic integrodifferential system in finite dimensional space. Using linear controllability theory, sufficient conditions ensuring complete controllability are derived based on controllability Grammian matrix which is defined by Mittag‐Leffler matrix function and fixed‐point techniques. Finally, two numerical examples are given to verify the proposed conditions.

Results on controllability of Hilfer fractional differential equations with infinite delay via measures of noncompactness

“…This system could be applicable to abundant models in wave propagation, signal processing, robotics, and so forth. It defines more about the theory and details of applications; also, the readers can review the books [1][2][3][4][5][6][7][8] and the research articles related to the theory of fractional differential systems [9][10][11][12][13][14][15][16]. Hilfer [17] introduced another type of fractional derivative involving Riemann-Liouville and Caputo fractional derivative.…”

Approximate and trajectory controllability of fractional stochastic differential equation with non‐instantaneous impulses and Poisson jumps

“…The significance of the approximate controllability lies in the fact that an arbitrary initial state can be steered toward an arbitrarily small neighborhood of any given target state by choosing a control function in the appropriate way. To get points of interest about this, one can see [18‐25] and the references cited therein. Research investigating trajectory controllability was started in 1996 by Raju K. George.…”

Results on approximate controllability of nondensely defined fractional neutral stochastic differential systems

“…Recently, controllability concerns for different sorts of nonlinear dynamical frameworks in infinite dimensional spaces became examined in numerous research articles by utilizing various types of techniques. A broad list of these distributions can be discovered in [2, 5, 6, 12, 14, 16–18, 20, 21, 26, 28, 30–32, 40–45, 48, 51, 55]. Also, the investigation of stochastic differential equations has pulled in great interest because of its applications in describing numerous issues in material science, biological science, mechanics, and so on.…”