Controllability of nonlinear stochastic neutral fractional dynamical systems

Abstract

In this paper, we obtain an equivalent nonlinear integral equation to the stochastic neutral fractional system with bounded operator. Using the integral equation, the sufficient conditions for ensuring the complete controllability of the stochastic fractional neutral systems with Wiener and Lévy noise are obtained. Banach's fixed point theorem is used to obtain the results. Examples are provided to illustrate the theory.

Relatively exact controllability of fractional stochastic delay system driven by Lévy noise

“…), which can be described as jumping process or more general Lévy noise. It is worth mentioning that the authors considered the controllability of the fractional neutral stochastic system with Lévy noise, in the work of Rajendran et al [37]. In the work of Su et al [38], approximate controllability of second order SDEs with Lévy process was presented.…”

“…Compared with some recent works [34, 36–44], the major contributions and difficulties of this article are mainly reflected in the following three aspects: • $$$ \left({C}_1\right) $$$ In the literatures [34, 36, 38, 40, 41], the literatures studied the controllability of dynamical systems without delay term in control, but the system we study has the control delay which is a continuous function regarding the variable $$$ t $$$. It is worth remark that time varying term make it harder to construct controllability Grammain matrix.…”

Cauchy Problem for a Stochastic Fractional Differential Equation with Caputo-Itô Derivative

“…However, in order to describe and forecast a real phenomenon, it is necessary to introduce a component that captures the random behavior caused by a major source of uncertainty, that usually propagates in time. When we add such a component, the model obtained is now governed by a stochastic fractional differential equation [6,7]. On the order hand, the Itô stochastic calculus has been applied in several fields of knowledge; such as, engineering, physics, biology, among others [8,9].…”

Controllability of fractional stochastic delay dynamical systems

“…In above all, control theory characterize a key role in both deterministic and stochastic control systems. In the last few years, controllability problems for different types of linear and nonlinear differential equations in finite and infinite dimensional spaces have been established in many publications [18,22,24,25]. Sakthivel et al [23] described a new set of sufficient conditions for approximate controllability of nonlinear fractional stochastic evolution equation in Hilbert spaces using some techniques and methods adopted from deterministic control problems.…”

“…Sakthivel et al [23] described a new set of sufficient conditions for approximate controllability of nonlinear fractional stochastic evolution equation in Hilbert spaces using some techniques and methods adopted from deterministic control problems. Rajendran et al [24] obtained the sufficient conditions for complete controllability of stochastic fractional neutral systems with Wiener and Lèvy noise. Meanwhile, Rajendran et al [25] studied the controllability of linear and nonlinear stochastic fractional systems with bounded operator having distributed delay in control.…”