Browsing by Author "Khedher, Khaled Mohamed"

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First-order impulsive differential systems: sufficient and necessary conditions for oscillatory or asymptotic behavior
(2021) Baleanu, Dumitru; Baleanu, Dumitru; Khedher, Khaled Mohamed; 56389
In this paper, we study the oscillatory and asymptotic behavior of a class of first-order neutral delay impulsive differential systems and establish some new sufficient conditions for oscillation and sufficient and necessary conditions for the asymptotic behavior of the same impulsive differential system. To prove the necessary part of the theorem for asymptotic behavior, we use the Banach fixed point theorem and the Knaster–Tarski fixed point theorem. In the conclusion section, we mention the future scope of this study. Finally, two examples are provided to show the defectiveness and feasibility of the main results. © 2021, The Author(s).
General solution and generalized Hyers-Ulam stability for additive functional equations
(2023) Baleanu, Dumitru; Arulselvam, Manimaran; Baleanu, Dumitru; Govindan, Vediyappan; Khedher, Khaled Mohamed; 56389
In this paper, we introduce new types of additive functional equations and obtain the solutions to these additive functional equations. Furthermore, we investigate the Hyers-Ulam stability for the additive functional equations in fuzzy normed spaces and random normed spaces using the direct and fixed point approaches. Also, we will present some applications of functional equations in physics. Through these examples, we explain how the functional equations appear in the physical problem, how we use them to solve it, and we talk about solutions that are not used for solving the problem, but which can be of interest. We provide an example to show how functional equations may be used to solve geometry difficulties.
Sawi transform and Hyers-Ulam stability of nth order linear differential equations
(2023) Baleanu, Dumitru; Ganesh, Anumanthappa; Santra, Shyam Sundar; Edwan, Reem; Baleanu, Dumitru; Khedher, Khaled Mohamed; 56389
The use of the Sawi transform has increased in the light of recent events in different approaches. The Sawi transform is also seen as the easiest and most effective way among the other transforms. In line with this, the research deals with the Hyers-Ulam stability of nth order differential equations using the Sawi transform. The study aims at deriving a generalised Hyers-Ulam stability result for linear homogeneous and non-homogeneous differential equations.