Publications Scientifiques
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Item Existence, uniqueness and abstract approach to hyers–ulam stability in banach lattice algebras and an application(Rocky Mountain Mathematics Consortium, 2023) Benkaci-Ali, NadirThe abstract equation of the form u = Ku · L(Fu) is investigated in this paper. By applying a fixed point theorem for the product of operators K and A = L(F) defined on a Banach lattice algebra E, we obtain existence and uniqueness results of fixed points of the operator T = K · A. Moreover, we state a sufficient condition on the spectral radius of a majorant linear mapping of L under which the equation u = T u has the L-Hyers–Ulam stability. As an application, the obtained results are used to prove existence and uniqueness of solutions and Hyers–Ulam stability of a (p1, p2,…, pn)-Laplacian hybrid fractional differential system. An example is also constructed to illustrate the main results. This work contains many new ideas, and gives a unified approach applicable to several types of differential and integral equations.Item Controllability of nonlocal Hilfer fractional delay dynamic inclusions with non-instantaneous impulses and non-dense domain(Springer, 2022) Boudjerida, Assia; Seba, DjamilaThe 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 outcomesItem Existence and uniqueness results for singular boundary value problem of weighted generalized fisher type differential equation(The Indonesian Mathematical Society, 2021) Benkaci-Ali, NadirIn this paper, we give existence and uniqueness results of nontrivial positive solution for the boundary value problem of the weighted and generalized Fisher's type differential equationItem 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, HamzaThis 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 exampleItem On the singular generalized Fisher-like equation with derivative depending nonlinearity(Elsevier, 2008) Djebali, Smaïl; Mebarki, KarimaItem Multiple unbounded positive solutions for three-point BVPs with sign-changing nonlinearities on the positive half-line(Springer, 2010) Djebali, Smaïl; Mebarki, KarimaItem Measure of noncompactness and hyperbolic partial fractional differential equations in banach spaces(2010) Benchohra, M.; Nieto, J.J.; Seba, DjamilaItem Bounded solutions for boundary value problems for fractional differential equations on a banach space and the half line(2011) Benchohra, M.; Seba, DjamilaItem Integral equations of fractional order with multiple time delays in Banach spaces(2012) Benchohra, M.; Seba, DjamilaIn 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