Browsing by Author "Sivasundaram, S."

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Advances in the Qualitative Theory of Integro-Differential Equations
(Nova Science Publishers, Inc., 2023) Tunç, O.; Sivasundaram, S.; Tunç, C.
This work investigates the advances from the past until now in the qualitative properties of solutions of linear and nonlinear integro-differential equations (IDEs). Here, we present an extensive literature on the qualitative properties of solutions, including asymptotic stability, uniform stability, instability and global uniform asymptotic stability of the zero solution, as well as boundedness, square integrability and existence of solutions to various linear and non-linear Volterra IDEs, without delay and with delay. We also present some applications of such equations in sciences and engineering. Some examples are given to illustrate the results of this work and show their applications. © 2023 Nova Science Publishers, Inc. All rights reserved.
Existence and Oscillatory Results for Caputo-Fabrizio Fractional Differential Equations and Inclusions
(Cambridge Scientific Publishers, 2021) Abbas, S.; Benchohra, M.; Sivasundaram, S.; Tunç, C.
In this paper; by using set-valued analysis, fixed point theory, and the method of upper and lower solutions, we prove some existence, oscillatory and nonoscillatory results for some classes of Caputo-Fabrizio fractional differential equations and inclusions © CSP - Cambridge, UK
New and Improved Criteria on Qualitative Results for Functional-Differential Systems
(Cambridge Scientific Publishers, 2022) Tunc¸, O.; Sivasundaram, S.; Atan, Ö.; Tunc¸, C.
In this paper, certain systems of functional differential equations (FDEs) with multiple constant delays are considered. Using the Lyapunov Krasovskiˇi functionals (LKFs), new and improved Lyapunov-Krasovskiˇi type fundamental criteria of uniformly stability (US), uniformly asymptotically stability (UAS), integrability and boundedness of solutions are obtained, respectively. Here, four new theorems are presented as complements of some related results in the past literature. Finally, we verify our results by giving two numerical examples with plots of paths of solutions. © CSP - Cambridge, UK; I&S - Florida, USA, 2022
Stability for Fractional Order Delay Singular Systems
(Cambridge Scientific Publishers, 2022) Yiğit, A.; Sivasundaram, S.; Tunç, C.
In this paper, a non-linear fractional order integro-singular system (FrOISS) is considered. Explicit criteria for asymptotic stability of that FrOISS are given via two new theorems. The studies of the paper are based on applications of two Lyapunov-Krasovskiǐ functionals (LKFs). In particular case, two examples and their simulations are included as applications of the results. By this work, some existing results are improved and generalized © CSP - Cambridge, UK; I&S - Florida, USA, 2022