Browsing by Author "Mesmouli, Mouataz Billah"

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Asymptotic Behavior of Levin-Nohel Nonlinear Difference System With Several Delays
(Amer inst Mathematical Sciences-aims, 2024) Mesmouli, Mouataz Billah; Tunc, Cemil; Hassan, Taher S.; Zaidi, Hasan Nihal; Attiya, Adel A.
In this manuscript, we considered a system of difference equations with delays and we established sufficient conditions to guarantee stability, asymptotic stability and exponential stability. In each type of stability, we created an appropriate space that guarantees us the existence of a fixed point that achieves the required stability.
Existence of Solutions and Ulam Stability Analysis of Implicit (P, Q)-Fractional Difference Equations
(Universal Wiser Publisher, 2025) Mesmouli, Mouataz Billah; Iambor, Loredana Florentina; Tunc, Osman; Hassan, Taher S.
This paper studies the existence theorems and Ulam stability results of solutions for implicit (p, q)-fractional difference equations. By applying Banach and Schauder fixed-point principles, we derive results related to the existence and uniqueness of solutions. Additionally, we analyze generalized Ulam-Hyers stability under (p, q)-Gronwall inequality. Key results are supported with illustrative examples, demonstrating the applicability of the proposed framework. Compared to previous studies restricted to the standard q-calculus, the present work introduces the (p, q)-Caputo fractional difference setting, which offers a more flexible and generalized approach. This novelty extends existing results and provides new perspectives for the analysis of stability and solvability of fractional systems.
Matrix Measure and Asymptotic Behaviors of Linear Advanced Systems of Differential Equations
(Springer international Publishing Ag, 2021) Mesmouli, Mouataz Billah; Tunc, Cemil
In this article, we study the convergence and exponential convergence of solutions for the linear system of advanced differential equations x'(t) + Sigma(N)(k=1) A(k) (t)x(t + h(k)(t)) = 0, t >= t(0) >= 0. The idea used here is to construct appropriate mappings by the fundamental matrix solution of x'(t) - A(t)x(t). Then, we apply the matrix measure and Banach fixed point theorem to obtain sufficient conditions satisfying convergence and exponential convergence of the considered system. The obtained theorems generalize and improve previous results of Dung (Acta Math Sci 35(3):610-618, 2015).