Ichrak BOUACIDA

Specialty: 
Mathematics
Department: 
Faculty: 
Campus: Ancien Campus
  • bouacida.ichrak@univ-guelma.dz
  • ichrakbouacida@gmail.com
Doctoral advisor: 
Google Scholar Link: 
Rersearchgate Link: 
ORCID: 

Thesis title

Doctoral thesis title: 
Fractional Order Control Systems and Their Applications

Thesis title (Ar)

Doctoral thesis title (Ar): 
أنظمة تحكم التطور ذات الرتب الكسرية وتطبيقاتها

Thesis title (Fr)

Doctoral thesis title (Fr): 
Systèmes de contrôle d'évolution d'ordres fractionnaires et leurs applications

keywords

Keywords: 
Approximate controllability, Fractional equation, fixed point theorem, semi-groups theory .

keywords (Ar)

Key words (Ar): 
.التحكم التقريبي ، المعادلة الكسرية ، نظرية النقطة الثابتة ، نظرية شبه المجموعات

keywords (Fr)

Key words (Fr): 
Contrôlabilité approchée, Equation fractionnaire, Théorème du point fixe, théorie du semi-groupe.

Abstract

Abstract: 

We study  differential equations of fractional orders in Hilbert spaces, basing on the fractional powers of the operators, the Laplace transform, the theory of semigroups and the fixed point technique to establish the existence result ( Mild, strong, weak, exact, optimal, almost periodic solutions,...) of classes of fractional differential equations (linear, semi-linear, quasi-linear and non-linear) (intero-differential, neutral, with delay,. . . ) having time-independent (dependent) closed operators defined in dense sets in Hilbert space and associated with initial conditions (non-local, impulsive), these operators are also supposed to generate semi-groups (systems 'evolution or resolving operators).

Abstract (Ar)

Abstract (Ar): 

ندرس المعادلات التفاضلية  ذات الرتب الكسرية في فضاءات هلبرث، بالاعتماد على القوى الكسرية للمؤثرات، وتحويل لابلاس، ونظرية  شبه المجموعات ، وتقنية النقطة الثابتة لتحديد نتيجة الوجود (خفيفة، قوية، ضعيفة، دقيقة، مثالية، حلول دورية تقريبًا،...) لفئات المعادلات التفاضلية الكسرية (الخطية، وشبه الخطية، وشبه الخطية، وغير الخطية) (التفاضلية البينية، المحايدة، مع تأخير،.. ) ذات وقت مستقل (تابع) العوامل المغلقة المحددة في مجموعات كثيفة في فضاء هيلبرث والمرتبطة بالشروط الأولية (غير المحلية، المندفعة)، من المفترض أيضًا أن تولد هذه العوامل شبه مجموعات (تطور الأنظمة أو عوامل حلها)

Abstract (Fr)

Abstract (Fr): 

Nous étudions les équations différentielles d'ordres fractionnaires dans les espaces de Hilbert, En basant sur les puissances fractionnaires des opérateurs, la transformée de Laplace, la théorie des semi-groupes et la technique du point fxe pour établir le résultat d'existence (Mild, fort, faible, solutions exactes, optimales, presque pèriodiques,. . . ) de classes d'équations différentielles fractionnaires (linéaires, semi-linéaires, quasi-linéaires et non linéaires) (intégro-différentielles, neutre, avec retard,. . . ) ayant des opérateurs fermés indépendants (dépendants) du temps définis dans des ensembles denses dans l'espace de Hilbert et associés  à des conditions initiales (non locales, impulsives), ces opérateurs sont également supposés générer des semi-groupes (systèmes d'évolution ou opérateurs résolvants).

Scientific publications

Scientific publications : 

 

  1. Controllability results for sobolev type Ψ-Hilfer fractional backward perturbed integro-differential equations in Hilbert space, Evol. Equ. Control Theory, Vol. 12, No. 1, February 2023, pp. 213-229.
  2. Null Controllability of  Ψ-Hilfer Implicit Fractioanl Integro-Differential Equations With Ψ-Hilfer Fractional Nonlocal Conditions, Vol. 12, No. 6, December 2023, pp. 1473-1491.     

Scientific conferences

Scientific conferences: 

 

 Internationales :

  1. RDOPDE 22 Recent Developments in Ordinary and Partial Differential Equations Topic : Fractional Differential Equations.At : Béjaia, 22-26 mai 2022. Implicit fractional integro-differential equations involving Ψ-Caputo fractional derivative.
  2. 6 th INTERNATIONAL HYBRID CONFERENCE ON MATHEMATICS“An Istanbul Meeting for World Mathematicians”21-24 June 2022, Istanbul, Turkey. Existence and Approximate Controllability of Mild Solutions for Ψ-Hilfer Fractional Integro-Differential Equations.
  3. The 6th International Workshop on Applied Mathematics and Modelling "WIMAM'2022". At: LMAM, University 8 may 1945 Guelma, Algeria.Affiliation: Université 8 mai 1945 - Guelma.  Trajectory controllability of nonlocal nonlinear system involving Ψ-Hilfer fractional derivative.
  4.  The 23rd International Pure Mathematics Conference 2023 (23rd IPMC 2023) on Algebra, Analysis and Geometry, Islamabad, 26- 28 August 2023.At: Islamabad, Pakistan. Approximate Controllability of Sobolev Type (k, Ψ)-Hilfer Fractional Integro-Differential Equations In Hilbert Space.
Nationales :
  1.  Third National Mathematics Seminar 2022, May 26, 2022.At : Frères Mentouri University, Constantine 1, Algeria. Existence And Uniqueness of  Mild Solution For Ψ-Hilfer Non  Local Fractional Evolution Equation.
  2.  The Second National Conference on Mathematics and its Applications (2nd SCNMA 2022) September 17-18, Bordj BouArréridj, Algeria. Null Controllability of Nonlocal Ψ -      Hilfer fractional Differential Equation.
  3.  Second National Conference on Applied Mathematics and Didactics SNCAMD2023.At: Constantine-Algeria. May 13th, 2023. Existence results of Mild solution for Sobolev   type Ψ-Hilfer hybrid fractional differential evolution equations.
  4.  The Second Online National Conference on Pure and Applied Mathematics "CNMPA 2023"At: Université Echahid Cheikh Larbi Tebessi-Tebessa, Algérie. Complete Controllability of Nonlinear (k; Ψ)-Hilfer Fractional Differential Equations In Hilbert Space