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

Kerboua, Mourad; Ellaggoune, Fateh; Băleanu, Dumitru

doi:10.1007/s13348-017-0207-5

Cited by 15 publications

(3 citation statements)

References 23 publications

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Nandhaprasadh,

Udhayakumar

2024

Contemp. Math.

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In this paper, the approximate boundary controllability of Hilfer fractional neutral stochastic differential inclusions with fractional Brownian motion (fBm) and Clarke’s subdifferential in Hilbert space is discussed. The existence of a mild solution of Hilfer fractional neutral stochastic differential inclusions with fractional Brownian motion and Clarke’s subdifferential is proved by using fractional calculus, compact semigroups, the fixed point theorem, stochastic analysis, and multivalued maps. The required conditions for the approximate boundary controllability of this system are defined according to a corresponding linear system that is approximately controllable. To demonstrate how our primary findings may be used, a final example is provided.

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Section: Introductionmentioning

confidence: 99%

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

Nandhaprasadh,

Udhayakumar

2024

Contemp. Math.

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Wang

Chen

Deng

et al. 2022

Math Methods in App Sciences

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In this paper, the Euler-Maruyama method is used to solve a class of nonlinear stochastic Volterra integral equations (SVIEs), which can be derived from stochastic fractional substantial integro-differential equations (SFSIDEs). The existence and uniqueness of the solution are proved for the nonlinear SVIEs ] , respectively, is established for the nonlinear SVIEs, which can be revised as supplemented theory results of our recent work (J Comput Appl Math 356 (2019) 377-390). In particular, it also closes a gap that was left on the convergence analysis in (J Comput Appl Math 317 (2017) 447-457). Finally, numerical experiments are given to illustrate the effectiveness of the presented method.

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“…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].…”

Section: Introductionmentioning

confidence: 99%

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

Yang

Deng²,

Ren

2020

Adv Differ Equ

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The stochastic resonance (SR) of a second-order harmonic oscillator subject to mass fluctuation and periodic modulated noise in viscous media is studied. The mass fluctuation noise is modeled as dichotomous noise and the memory of viscous media is characterized by fractional power kernel function. By using the Shapiro-Loginov formula and Laplace transform, we got the analytical expression of the first moment of the steady-state response and studied the relationship between the system response and the system parameters in the long-time limit. The simulation results show the non-monotonic dependence between the response amplitude and the input signal frequency, noise parameters of the system, etc, which indicates that the bona fide resonance and the generalized SR phenomena appear. Furthermore, the mass fluctuation noise, modulation noise, and the fractional order work together, producing more complex dynamic phenomena than the integral-order system. For example, there is a transition from bimodal resonance to unimodal resonance between the amplitude and the driving frequency under different fractional orders.

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

Cited by 15 publications

References 23 publications

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

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

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

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

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