Browsing by Author "Hassan, T.S."

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Existence of Solutions and Ulam Stability Analysis of Implicit (P, Q)-Fractional Difference Equations
(Universal Wiser Publisher, 2025) Mesmouli, M.B.; Iambor, L.F.; Tunç, O.; Hassan, T.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. © 2025 Loredana Florentina Iambor, et al.
On the Fixed Point Theorem for Large Contraction Mappings With Applications To Delay Fractional Differential Equations
(Multidisciplinary Digital Publishing Institute (MDPI), 2024) Mesmouli, M.B.; Akın, E.; Iambor, L.F.; Tunç, O.; Hassan, T.S.
This paper explores a new class of mappings and presents several fixed-point results for these mappings. We define these mappings by combining well-known mappings in the literature, specifically the large contraction mapping and Chatterjea’s mapping. This combination allows us to achieve significant fixed-point results in complete metric spaces, both in a continuous and a non-continuous sense. Additionally, we provide an explicit example to validate our findings. Furthermore, we discuss a general model for fractional differential equations using the Caputo derivative. Finally, we outline the benefits of our study and suggest potential areas for future research. © 2024 by the authors.