Browsing by Author "Seba, Djamila"

Now showing 1 - 20 of 32

Almost and weakly nsr, nsm and nsh spaces
(Department of Pure Mathematics, Ferdowsi University of Mashhad Tusi Mathematical Research Group (TMRG), 2021) Lakehal, Rachid; Kočinac, Ljubiša D. R.; Seba, Djamila
We introduce and study some new types of star-selection princi-ples (almost and weakly neighborhood star-Menger, neighborhood star-Rothb-erger, and neighborhood star-Hurewicz). We establish some properties of theseselection principles and their relations with other selection properties of topo-logical spaces. The behavior of these classes of spaces under certain kinds ofmappings is also considered
Analysis of energy dissipation in hyperbolic problems influenced by internal and boundary control mechanisms
(Taylor and Francis Ltd., 2024) Laoubi, Karima; Seba, Djamila
This article primarily focuses on the rational stabilisation of the wave equation, supplied with a second-order dynamical boundary condition of hyperbolic type, while considering an additional internal damping mechanism within the specified ring. To achieve rational decay rates of the associated energy, it is imperative to exponentially stabilise a portion of the domain using a global Ingham's-type estimate. This paper will subsequently illustrate how this partially localised exponential stabilisation, combined with a Bessel analysis, leads to a rational decrease in the overall energy of the system considered.
Approximate controllability of hybrid Hilfer fractional differential inclusions with non-instantaneous impulses
(Elsevier, 2021) Boudjerida, Assia; Seba, Djamila
This paper deals with the approximate controllability of a class of non-instantaneous impulsive hybrid systems for fractional differential inclusions under Hilfer derivative of order 1<σ<2 and type 0≤ζ≤1, on weighted spaces. As an alternative to the Wright function which is defined only when 0<σ<1, we make use of a family of general fractional resolvent operators to give a proper form of the mild solution. This latter is consequently formulated by Laplace transform, improving and extending important results on this topic. Based on known facts about fractional calculus and set-valued maps, properties of the resolvent operator, and a hybrid fixed point theorem for three operators of Schaefer type, the existence result and the approximate controllability of our system is achieved. An example is given to demonstrate the effectiveness of our result
Bounded solutions for boundary value problems for fractional differential equations on a banach space and the half line
(2011) Benchohra, M.; Seba, Djamila
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
Controllability of coupled systems for impulsive φ- Hilfer fractional integro-differential inclusions
(Taylor & Francis, 2020) Boudjerida, Assia; Seba, Djamila; N'Guérékata, G. M.
This paper studies the controllability of a coupled system for a class of impulsive fractional integro-differential inclusions involving φ-Hilfer fractional derivative and subject to coupled nonlocal integral initial conditions in the case of convex set-valued maps. Some auxiliary conditions are introduced in order to apply a fixed point theorem due to Bohnenblust–Karlin. An illustrative example is provided to exemplify our theoretical results
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
Controllability of nonlocal Hilfer fractional delay dynamic inclusions with non-instantaneous impulses and non-dense domain
(Springer, 2022) Boudjerida, Assia; Seba, Djamila
The controllability of a class of nondensely defined fractional dynamic delay inclusions containing Hilfer fractional derivative, nonlocal conditions, and non-instantaneous impulses in abstract spaces is investigated without compactness assumption. The existence of an integral solution and the controllability for the given problem are established relying on a condensing fixed point theorem of multivalued maps. In support, an example is given to clarify the obtained theoretical outcomes
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.
Controllability results for nondensely defined impulsive fractional-order functional semilinear differential inclusions in abstract space
(American Institute of Physics, 2019) Boudjerida, Assia; Seba, Djamila; Laoubi, Karima
In this work, we prove the controllability result of integral solutions defined on a real compact interval for a class of impulsive functional differential inclusions with fractional order and nonlocal conditions, in the case when the linear part is a non-densely defined operator and satisfies the Hille-Yosida condition. The main tool is an appropriate fixed point theorem, integrated semigroup, and the known facts about fractional calculus
Controllability results of Fractional Non-instantaneous Impulsive Semilinear Differential Inclusions with Infinite delay
(IEEE, 2020) Boudjerida, Assia; Seba, Djamila; Laoubi, Karima
In the content of this paper, we will talk over the controllability results for an active type of impulsive fractional semilinear differential inclusions with non-instantaneous impulses and infinite delay by means of caputo fractional derivative. To establish our principal results we give some sufficient hypotheses, we use the Known facts about multivalued map and fractional calculus, and we employing the different techniques of fixed point theorem
An efficient approach for solving differential equations in the frame of a new fractional derivative operator
(MDPI, 2023) Attia, Nourhane; Akgül, Ali; Seba, Djamila; Nour, Abdelkader; la Sen, Manuel De; Bayram, Mustafa
Recently, a new fractional derivative operator has been introduced so that it presents the combination of the Riemann–Liouville integral and Caputo derivative. This paper aims to enhance the reproducing kernel Hilbert space method (RKHSM, for short) for solving certain fractional differential equations involving this new derivative. This is the first time that the application of the RKHSM is employed for solving some differential equations with the new operator. We illustrate the convergence analysis of the applicability and reliability of the suggested approaches. The results confirm that the RKHSM finds the true solution. Additionally, these numerical results indicate the effectiveness of the proposed method
An efficient numerical technique for a biological population model of fractional order
(ELSEVIER, 2021) Attia, Nourhane; Akgül, Ali; Seba, Djamila; Nour, Abdelkader
In the present paper, a biological population model of fractional order (FBPM) with one carrying capacity has been examined with the help of reproducing kernel Hilbert space method (RKHSM). This important fractional model arises in many applications in computational biology. It is worth noting that, the considered FBPM is used to provide the changes that is made on the densities of the predator and prey populations by the fractional derivative. The technique employed to construct new numerical solutions for the FBPM which is considered of a system of two nonlinear fractional ordinary differential equations (FODEs). In the proposed investigation, the utilised fractional derivative is the Caputo derivative. The most valuable advantages of the RKHSM is that it is easily and fast implemented method. The solution methodology is based on the use of two important Hilbert spaces, as well as on the construction of a normal basis through the use of Gram-Schmidt orthogonalization process. We illustrate the high competency and capacity of the suggested approach through the convergence analysis. The computational results, which are compared with the homotopy perturbation Sumudu transform method (HPSTM), clearly show: On the one hand, the effect of the fractional derivative in the obtained outcomes, and on the other hand, the great agreement between the mentioned methods, also the superior performance of the RKHSM. The numerical computational are presented in illustrated graphically to show the variations of the predator and prey populations for various fractional order derivatives and with respect to time.
The Henstock-Kurzweil-Pettis integral and multiorders fractional differential equations with impulses and multipoint fractional integral boundary conditions in Banach spaces
(Wiley, 2021) Seba, Djamila; Habani, Sadek; Benaissa, Abbes; Rebai, Hamza
This paper is devoted to the existence of weak solutions for a multipoint fractional integral boundary value problem of an impulsive nonlinear differential equation involving multiorders fractional derivatives and deviating argument. We make use of an appropriate fixed point theorem combined with the technique of measures of weak noncompactness. Our investigation is considered in a Banach space. The applicability of the obtained results is illustrated by an example
Integral equations of fractional order with multiple time delays in Banach spaces
(2012) Benchohra, M.; Seba, Djamila
In this article, we give sufficient conditions for the existence of solutions for an integral equation of fractional order with multiple time delays in Banach spaces. Our main tool is a fixed point theorem of Mönch type associated with measures of noncompactness. Our results are illustrated by an example. © 2012 Texas State University - San Marcos
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.
Local bifurcation analysis of one parameter in the greitzer’s model with a general compressor characteristic
(Springer, 2022) Naima Meskine, Naima; Kessal, Mohand; Seba, Djamila
Based on the Greitzer’s reduced model, an analytical study on the instabilities phenomena of the operating point is presented using some basic properties of the nonlinear dynamic system. Moreover, a proposal of a general compressor characteristic curve, that suits the stationary system, is given. The Routh–Hurwitz theorem is applied to determine the stability conditions on the model parameters. An analysis along with a discussion is presented when the compression system goes to the Hopf bifurcation point during surge. For the Hopf bifurcation case, an approximate expression, for the periodic cycle of the system’s solution from the equilibrium point, is obtained and the direction is determined using Lyapunov’s stability theory. A numerical simulation is executed to illustrate the theoretical results
Measure of noncompactness and fractional differential equations in banach spaces
(Dynamic Publishers, 2008) Benchohra, M.; Henderson, J.; Seba, Djamila
Measure of noncompactness and hyperbolic partial fractional differential equations in banach spaces
(2010) Benchohra, M.; Nieto, J.J.; Seba, Djamila
Measure of noncompactness and partial differential equations involving riemann-liouville fractional derivative
(Dynamic Publishers, 2010) Benchohra, M.; Seba, Djamila