Publications Scientifiques

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Existence, uniqueness and abstract approach to hyers–ulam stability in banach lattice algebras and an application
(Rocky Mountain Mathematics Consortium, 2023) Benkaci-Ali, Nadir
The 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.
Existence and uniqueness results for singular boundary value problem of weighted generalized fisher type differential equation
(The Indonesian Mathematical Society, 2021) Benkaci-Ali, Nadir
In 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 equation