Approximate controllability of Sobolev type fractional stochastic nonlocal nonlinear differential equations in Hilbert spaces

Kerboua, Mourad; Debbouche, Amar; Băleanu, Dumitru

doi:10.14232/ejqtde.2014.1.58

Cited by 23 publications

(11 citation statements)

References 41 publications

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“…Fractional differential equations have been recognized as one of the best tools to be applied in interdisciplinary field such as viscoelastic materials and electromagnetic problems. For more details, one can refer to [18][19][20][21][22][23][24][25][26][27][28][29] and the references given therein. Recently, there have been some advances in ILC theory of fractional differential systems [30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

On the iterative learning control of fractional impulsive evolution equations in Banach spaces

Debbouche

Wang

2015

Math Methods in App Sciences

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In this paper, we study P‐type, PIα‐type, and D‐type iterative learning control for fractional impulsive evolution equations in Banach spaces. We present triple convergence results for open‐loop iterative learning schemes in the sense of λ‐norm through rigorous analysis. The proposed iterative learning control schemes are effective to fractional hybrid infinite‐dimensional distributed parameter systems. Finally, an example is given to illustrate our theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 99%

On the iterative learning control of fractional impulsive evolution equations in Banach spaces

Debbouche

Wang

2015

Math Methods in App Sciences

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“…On the other hand, a Sobolev-type equation appears in a variety of physical problems such as flow of fluid through fissured rocks, thermodynamics, propagation of long waves of small amplitude and so on [37][38][39]. The existence result of mild solutions of fractional integrodifferential equations of Sobolev type with nonlocal condition in a separable Banach space was studied by using the theory of propagation families as well as the theory of the measures of noncompactness and the condensing maps [6].…”

Section: + U(t) = Au(t) + F (T U(t)) T ∈ (0 B] Imentioning

confidence: 99%

Existence of mild solutions for Sobolev-type Hilfer fractional evolution equations with boundary conditions

Gou

2018

Bound Value Probl

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This paper is concerned with the fractional differential equations of Sobolev type with boundary conditions in a Banach space. With the help of the properties of Hilfer fractional calculus, the theory of propagation families as well as the theory of the measure of noncompactness and fixed point methods, we obtain the existence results of mild solutions for Sobolev-type fractional evolution differential equations involving the Hilfer fractional derivative. Finally, an example is presented to illustrate the main result.

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“…Kerboua et al [13] introduced a new notion called fractional stochastic nonlocal condition for establishing approximate controllability of class of fractional stochastic nonlinear differential equations of Sobolev type in Hilbert spaces using Hölder's inequality, fixed point technique, fractional calculus, stochastic analysis and methods adopted directly from deterministic control problems.…”

Section: D Q T [Lx (T)] = (M + M) X (T) + Bu (T) + F (T X (T))mentioning

confidence: 99%

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

2017

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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.

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Approximate controllability of Sobolev type fractional stochastic nonlocal nonlinear differential equations in Hilbert spaces

Cited by 23 publications

References 41 publications

On the iterative learning control of fractional impulsive evolution equations in Banach spaces

On the iterative learning control of fractional impulsive evolution equations in Banach spaces

Existence of mild solutions for Sobolev-type Hilfer fractional evolution equations with boundary conditions

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

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