Browsing by Author "Pinelas, S."

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Existence and Stabilization for Impulsive Integro-Differential Equations of Second-Order With Multiple Kernels and Delays
(John Wiley and Sons Ltd, 2025) Pinelas, S.; Tunç, Osman; Tunç, Cemil
The mathematical formulation of many dynamic systems naturally culminates in the second-order impulsive delay integro-differential equations (IPDIDEs). This study focuses on existence and stabilization results for the second-order IPDIDEs containing multiple time delays. Initially, the existence of a solution is established using Schaefer's fixed point theorem. Following this, the stabilization result is derived through the method of Lyapunov–Krasovskii functionals. The findings of this study improve upon and extend several well-known results in the existing literature. In a specific case, we present an example that demonstrates the applicability of our results. © 2025 Elsevier B.V., All rights reserved.
On System of Variable Order Nonlinear P-Laplacian Fractional Differential Equations With Biological Application
(MDPI, 2023) Khan, H.; Alzabut, J.; Gulzar, H.; Tunç, O.; Pinelas, S.
The study of variable order differential equations is important in science and engineering for a better representation and analysis of dynamical problems. In the literature, there are several fractional order operators involving variable orders. In this article, we construct a nonlinear variable order fractional differential system with a p-Laplacian operator. The presumed problem is a general class of the nonlinear equations of variable orders in the ABC sense of derivatives in combination with Caputo’s fractional derivative. We investigate the existence of solutions and the Hyers–Ulam stability of the considered equation. The presumed problem is a hybrid in nature and has a lot of applications. We have given its particular example as a waterborne disease model of variable order which is analysed for the numerical computations for different variable orders. The results obtained for the variable orders have an advantage over the constant orders in that the variable order simulations present the fluctuation of the real dynamics throughout our observations of the simulations. © 2023 by the authors.