Stochastic fractional perturbed control systems with fractional Brownian motion and Sobolev stochastic non local conditions

Abstract

This paper investigates the approximate controllability for Sobolev type stochastic perturbed control systems of fractional order with fractional Brownian motion and Sobolev fractional stochastic nonlocal conditions in a Hilbert space, A new set of sufficient conditions are established by using semigroup theory, fractional calculus, stochastic integrals for fractional Brownian motion, Banach's fixed point theorem. The results are obtained under the assumption that the associated linear system is approximately controllable. Finally, an example is also given to illustrate the obtained theory.

Hilfer Fractional Neutral Stochastic Differential Inclusions with Clarke’s Subdifferential Type and fBm: Approximate Boundary Controllability

“…Ahmed et al [28] investigated the approximate controllability of nonlocal Sobolev-type neutral fractional stochastic differential equations with fractional Brownian motion and Clarke subdifferential. Mourad et al [29] investigated stochastic fractional perturbed control systems with fractional Brownian motion and Sobolev stochastic nonlocal conditions. Mourad [30] established the approximate controllability of fractional neutral stochastic evolution equations in Hilbert spaces with fractional Brownian motion.…”

A sharp error estimate of Euler‐Maruyama method for stochastic Volterra integral equations

“…4,[7][8][9] On the other hand, due to the existence of ubiquitous noise factors in nature, stochastic integro-differential equations emerge in biology, 10 finance, 11,12 and more. [13][14][15] Nowadays, stochastic fractional models such as stochastic Volterra integral equations (SVIEs) and stochastic fractional integro-differential equations (SFIDEs) have been increasingly employed in diverse areas such as problems in science and engineering, 16,17 mathematical finance, 18 dynamical systems in physics, 19 biology, 20,21 and medical technology. 22 However, in many cases, due to the presence of random factors in models, the exact solutions to these problems are hard to obtain.…”

Stochastic resonance of fractional-order Langevin equation driven by periodic modulated noise with mass fluctuation

“…The literature indicates that the FLE has much richer dynamic behaviors than the classical harmonic oscillator and is more beneficial to the description of real environments. Some scholars have also made attempts and explorations in this respect, and studies have shown that fractional dynamical systems based on fractional-order differential equations tend to have more abundant dynamic phenomena than integerorder stochastic dynamical systems under similar conditions [30][31][32][33][34].…”