Browsing by Author "Aimene, Djihad"

Filter results by typing the first few letters
Now showing 1 - 6 of 6
  • No Thumbnail Available
    Item
    Contribution to the study of the controllability of semilinear differential equations of fractional order
    (Université M'hamad Bougara : Faculté des Sciences, 2021) Aimene, Djihad; Seba, Djamila(Directeur de thèse)
    In view of the increased interest that the Kalman concept has received since the 1960s, this thesis is dedicated to contributing to the development of research on the controllability of a class of semilinear differential systems of fractional order with the impulsive condition in abstract spaces, by applying the techniques of fixed point theory and concepts of semigroup theory and define an admissible set of necessary and sufficient conditions to prove the existence of mild solutions and are renewed in each time with what suits the studied system. During this doctoral thesis, we rely on the use of three different definitions of fractional derivatives and discuss their fundamental properties, as well as highlighting the most important basic mathematical principles and necessary theoretical concepts to reach the desired results. This thesis permeates a valuable set of practical examples to prove the proposed approach and further clarify the given purpose
  • No Thumbnail Available
    Item
    Controllability for Semilinear Fractional Integro-differential Systems with Deviated Argument in Banach Spaces
    (IEEE, 2020) Aimene, Djihad; Seba, Djamila; Laoubi, Karima
    In this work we will rely on the technique application of semigroup theory and fixed point theorem “Banach contraction” to demonstrate that there exists a mild solution to this type of controllability for semilinear fractional integro-differential equations with deviated arguments in Banach spaces
  • No Thumbnail Available
    Item
    Controllability of impulsive fractional functional evolution equations with infinite state-dependent delay in Banach spaces
    (Wiley, 2021) Aimene, Djihad; Seba, Djamila; Laoubi, Karima
    Many evolutionary processes from various fields of physical and engineering sciences undergo abrupt changes of state at certain moments of time between intervals of continuous evolution. These processes are more suitably modeled by impulsive differential equations. In this paper, we study the controllability of an impulsive fractional differential equation with infinite state-dependent delay in an arbitrary Banach space. We apply semigroup theory and Schaefer fixed point theorem. As an application, we include an example to illustrate the theory
  • No Thumbnail Available
    Item
    Controllability of semilinear impulsive Atangana-Baleanu fractional differential equations with delay
    (Elsevier, 2019) Aimene, Djihad; Baleanu, D.; Seba, Djamila
    We discuss the controllability of semilinear differential equations of fractional order with impulses and delay. We make use of the Atangana-Baleanu derivative. Our main tools are semigroup theory, the fixed point theorem due to Darbo and their combination with the properties of measures of noncompactness. Our abstract results are well supported by an illustrative example.
  • No Thumbnail Available
    Item
    Local and global existence of mild solutions of time-fractional Navier–Stokes system posed on the Heisenberg group
    (Birkhauser, 2021) Kirane, Mokhtar; Aimene, Djihad; Seba, Djamila
    This paper is a development of the results and techniques of the two papers (Carvalho-Neto and Planas in J Differ Equ 259:2948–2980, 2015; Oka in J Math Anal Appl 473:382–407, 2019) for the aim of addressing the existence and uniqueness of local and global mild solutions, on the Heisenberg group Hd, of the time-fractional Navier–Stokes system with time derivative of order α∈ (0 , 1). The proof relies on Schaefer’s fixed point theorem. © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
  • No Thumbnail Available
    Item
    On approximate controllability of impulsive fractional semilinear systems with deviated argument in hilbert spaces
    (InforMath Publishing Group, 2020) Aimene, Djihad
    In this paper we apply a fixed-point theorem to study the existence and uniqueness of a mild solution and the approximate controllability of a fractional order impulsive differential equation with deviated argument in Hilbert spaces. An example is provided to show the effectiveness of the theory