Browsing by Author "Debbouche, Amar"

Now showing 1 - 6 of 6

Citation - WoS: 22
Citation - Scopus: 30
Approximate Controllability of Sobolev Type Fractional Stochastic Nonlocal Nonlinear Differential Equations in Hilbert Spaces
(Univ Szeged, Bolyai institute, 2014) Debbouche, Amar; Baleanu, Dumitru; Kerboua, Mourad
We introduce a new notion called fractional stochastic nonlocal condition, and then we study approximate controllability of class of fractional stochastic nonlinear differential equations of Sobolev type in Hilbert spaces. We use Holder's inequality, fixed point technique, fractional calculus, stochastic analysis and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions is formulated and proved for the fractional stochastic control system to be approximately controllable. An example is given to illustrate the abstract results.
Citation - WoS: 29
Citation - Scopus: 32
Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems in Hilbert Spaces
(Hindawi Ltd, 2013) Debbouche, Amar; Baleanu, Dumitru; Kerboua, Mourad
We study a class of fractional stochastic dynamic control systems of Sobolev type in Hilbert spaces. We use fixed point technique, fractional calculus, stochastic analysis, and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions for approximate controllability is formulated and proved. An example is also given to provide the obtained theory.
Citation - WoS: 206
Citation - Scopus: 230
Controllability of Fractional Evolution Nonlocal Impulsive Quasilinear Delay Integro-Differential Systems
(Pergamon-elsevier Science Ltd, 2011) Baleanu, Dumitru; Debbouche, Amar
In this work, the controllability result of a class of fractional evolution nonlocal impulsive quasilinear delay integro-differential systems in a Banach space has been established by using the theory of fractional calculus, fixed point technique and also we introduced a new concept called (alpha, u)-resolvent family. As an application that illustrates the abstract results, an example is given. (C) 2011 Elsevier Ltd. All rights reserved.
Citation - WoS: 26
Citation - Scopus: 26
Exact Null Controllability for Fractional Nonlocal Integrodifferential Equations Via Implicit Evolution System
(Hindawi Publishing Corporation, 2012) Baleanu, Dumitru; Debbouche, Amar
We introduce a new concept called implicit evolution system to establish the existence results of mild and strong solutions of a class of fractional nonlocal nonlinear integrodifferential system, then we prove the exact null controllability result of a class of fractional evolution nonlocal integrodifferential control system in Banach space. As an application that illustrates the abstract results, two examples are provided.
Citation - WoS: 25
Citation - Scopus: 29
Existence of Solutions for Fractional Differential Inclusions With Separated Boundary Conditions in Banach Space
(Hindawi Ltd, 2013) Debbouche, Amar; Baleanu, Dumitru; Bragdi, Mabrouk
We discuss the existence of solutions for a class of some separated boundary differential inclusions of fractional orders 2 < alpha < 3 involving the Caputo derivative. In order to obtain necessary conditions for the existence result, we apply the fixed point technique, fractional calculus, and multivalued analysis.
Citation - WoS: 46
Citation - Scopus: 58
Nonlocal Nonlinear Integrodifferential Equations of Fractional Orders
(Springer, 2012) Baleanu, Dumitru; Agarwal, Ravi P.; Debbouche, Amar
In this paper, Schauder fixed point theorem, Gelfand-Shilov principles combined with semigroup theory are used to prove the existence of mild and strong solutions for nonlinear fractional integrodifferential equations of Sobolev type with nonlocal conditions in Banach spaces. To illustrate our abstract results, an example is given. MSC: 35A05, 34G20, 34K05, 26A33.