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 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 Positive Solution for the Integral and Infinite Point Boundary Value Problem for Fractional-Order Differential Equation Involving a Generalized ϕ-Laplacian Operator(Hindawi, 2020) Benkaci-Ali, NadirIn this paper, we establish the existence of nontrivial positive solution to the following integral-infinite point boundary-value problem involving -Laplacian operator where is a continuous function and is the Riemann-Liouville derivative for . By using some properties of fixed point index, we obtain the existence results and give an example at last.Item Positive solutions for a p(t)-laplacian three point boundary value problem(2013) Benkaci-Ali, Nadir; Benmezai, A.; Henderson, J.Item Eigenvalue criteria for existence of positive solutions to singular third-order BVPs via the index-jump property(2013) Benkaci-Ali, Nadir; Benmezai, A.; Ntouyas, S.K.Item Positive solution for a p(t)-Laplacian three point boundary value problem on the half line(Dynamic Publishers, 2013) Benkaci-Ali, Nadir; Benmezai, A.; Ntouyas, S.K.Item Positive solution for fourth order four-point BVPs involving weighted p(t)-Laplacian like operator(Institute of Advanced Scientific Research, 2014) Benkaci-Ali, Nadir; Benmezai, A.