Browsing by Author "Altun, Y."

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Discussion on the Solutions To Nonlinear Singular Systems With Delay Via Lyapunovkrasovski Approach
(Cambridge Scientific Publishers, 2024) Altun, Y.
In this paper, some qualitative behaviors of nonlinear singular systems (NSSs) with time-varying delays are investigated. By means of the Lyapunov-Krasovski functional (LKF) approach, some solution estimates for the considered systems are generated. The obtained solution estimates allow us to evaluate some qualitative behaviors of the solutions. Several simple examples with simulation are given to show the feasibility of proposed method on current results using MATLAB software. In this paper, we expand and improve some of the results in the related to literature. 2010 Mathematics Subject Classification: 34K20, 93C10. © CSP - Cambridge, UK; I&S - Florida, USA, 2024
Improved Results on the Stability Analysis of Linear Neutral Systems With Delay Decay Approach
(John Wiley and Sons Ltd, 2020) Altun, Y.
In this paper, the investigation of the asymptotical stability of linear neutral systems with time-varying delay has been presented. In order to achieve the desired results, the integral inequality approach was used to express relationships between terms of Newton-Leibniz formula technique and was constructed an appropriate Lyapunov-Krasovskii functional. By improving a delay decay approach, the stability criteria for the zero solution of system were formulated as linear matrix inequalities (LMIs) which can be easily solved. Two numerical examples have been given to show the applicability of established assumptions and the effectiveness of proposed method by MATLAB-Simulink. © 2019 John Wiley & Sons, Ltd.
Lmi Based Approach To Asymptotically Stability Analysis for Fractional Neutral-Type Neural Networks With Riemann Liouville Derivative
(Cambridge Scientific Publishers, 2022) Altun, Y.
By this research paper, we search the asymptotically stability of fractional neutral-type neural networks with Riemann Liouville (RL) derivative. The activation functions discussed in this research are assumed to be globally Lipschitz continuous. The arguments of proposed stability requirements are based upon the linear matrix inequalities (LMIs) approach, which can be easily checked using the Lyapunov-Krasovskii functional. Finally, two simple examples and their simulations are presented to demonstrate that the obtained results are computationally flexible and effective © CSP - Cambridge, UK; I&S - Florida, USA, 2022
A Note on the Asymptotic Stability of Solutions of Non-Linear Neutral Systems With Variable Delay
(Cambridge Scientific Publishers, 2019) Altun, Y.
In this study, we are presented some sufficient conditions for the asymptotic stability of solutions of a non-linear neutral system with variable delay. The approaches to obtaining these sufficient conditions are based on the Lyapunov-Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) technique. Criteria are derived for asymptotic analysis of solutions of the system considered. Consequently, two numerical examples are given to show the effectiveness and applicability of proposed method by MATLAB-Simulink. © CSP - Cambridge, UK; I & S - Florida, USA, 2019.
A Numerical Treatment Through Bayesian Regularization Neural Network for the Chickenpox Disease Model
(Elsevier Ltd, 2025) Sabir, Z.; Mehmood, M.A.; Umar, M.; Salahshour, S.; Altun, Y.; Arbi, A.; Ali, M.R.
Objectives: The current research investigations designates the numerical solutions of the chickenpox disease model by applying a proficient optimization framework based on the artificial neural network. The mathematical form of the chickenpox disease model is divided into different categories of individuals, susceptible, vaccinated, infected, exposed, recovered, and infected with/without complications. Method: The construction of neural network is performed by using the single hidden layer and the optimization of Bayesian regularization. A dataset is assembled using the explicit Runge-Kutta technique for reducing the mean square error using the training 76 %, while 12 %, 12 % for validation and testing. The whole stochastic procedure is based on logistic sigmoid fitness function, single hidden layer structure with thirty neurons, along with the optimization capability of Bayesian regularization. Finding: The designed procedure's correctness and reliability is observed by results matching, negligible absolute error around 10−04 to 10−06, regression, error histogram, and state transmission. Moreover, the best performance values based on the mean square error are performed as 10−09 to 10−11. Novelty: The current neural network framework using the construction of a single hidden layer and the optimization of Bayesian regularization is applied first time to solve the chickenpox disease model. © 2025 Elsevier Ltd
On Exponential Stability of Solutions of Nonlinear Neutral Differential Systems With Discrete and Distributed Variable Lags
(Cambridge Scientific Publishers, 2019) Altun, Y.; Tunç, C.
In this paper, we investigated the exponential stability for nonlinear neutral differential system with multiple retarded arguments. To reach the desired results, we used a Lyapunov-Krasovskii functional for exponential stability criterions of the zero solution of system. These stability criteria obtained are formulated as matrix inequalities which can be easily solved. The results obtained in this study extend and improves some related ones in the literature. © CSP - Cambridge, UK, 2019.
On the Estimates for Solutions of a Nonlinear Neutral Differential System With Periodic Coefficients and Time-Varying Lag
(Palestine Polytechnic University, 2019) Altun, Y.; Tunç, C.
In this paper, we consider a nonlinear neutral differential system with periodic coefficients and time-varying lag. We obtain new estimates to characterize the exponential decay of solutions of that system at +∞ and depending on the norms of the powers of a constant matrix D. To reach the desirable results, we use a Lyapunov-Krasovskii functional and give an example to show applicability of the constructed assumptions. We also use MATLAB-Simulink to show the behaviors of the paths of the solutions of the system considered in the special case. © Palestine Polytechnic University-PPU 2019.
On the Exponential Stability of Neutral Linear Systems With Variable Delays
(Springer, 2021) Altun, Y.; Tunç, C.
We investigate the exponential stability of a linear system of neutral-type with variable time lags. By using the Newton–Leibniz formula and a Lyapunov–Krasovskii functional, we prove two results on the exponential stability of solutions. The stability criteria are stated in the form of linear matrix inequalities. By using the MATLAB-Simulink software, we present two numerical examples illustrating the applicability of our assumptions. The obtained results extend and generalize the already known results available from the related literature. © 2021, Springer Science+Business Media, LLC, part of Springer Nature.
On the Nature of Solutions of Neutral Differential Equations With Periodic Coefficients
(Natural Sciences Publishing USA, 2017) Tunç, C.; Altun, Y.
By this work, we construct certain specific assumptions guaranteeing the asymptotic stability (AS) of trivial solution to a retarded linear neutral differential equation with periodic coefficients, and we estimate the decay rate of the solutions of the considered equation. To reach the desirable results, we benefit from a Lyapunov functional. We give an example to show applicability of the constructed assumptions and use MATLAB-Simulink to show the behaviors of the paths of the solutions of the considered equation. © 2017 NSP.
Some Results on the Stability of Solutions of Neutral Type Systems With Variable Delay
(Cambridge Scientific Publishers, 2022) Altun, Y.
In this research, we obtained new results for some qualitative behaviors of solutions of first order delayed neutral type systems by constructing a suitable Lyapunov functional. Based on the Lyapunov-Krasovskii functional approach, we give new results about the stability of a class of neutral type differential systems under some assumptions. The results obtained under the constructed assumptions allow us to conclude whether the solutions are stable or not. The results in this study are novel and contribute to the related literature under less restrictive conditions. © CSP - Cambridge, UK; I&S - Florida, USA, 2022
Stability Conditions for Fractional Differential and Neutral Systems With Discrete and Distributed Constant Delay Components
(Cambridge Scientific Publishers, 2021) Altun, Y.
In this manuscript, the stability conditions for Riemann-Liouville (R-L) fractional differential and neutral systems with discrete and distributed constant delay components are studied. We define the meaningful Lyapunov functional to obtain the desired results. The stability criteria for zero solution of differential equation and system are expressed in the form linear matrix inequalities (LMIs) which can be easily tested. Finally, some numerical examples are presented to illustrate the effectiveness of determined assumptions and proposed method by using MATLAB-Simulink. © CSP - Cambridge, UK; I&S - Florida, USA, 2021
Stability of Certain Neutral Type Differential Equation and Numerical Experiment Via Differential Transform Method
(Bayram Sahin, 2021) Altun, Y.
In this study, we obtain both the asymptotically stability and the numerical solution of first order neutral type differential equation with multiple retarded arguments. We first obtain sufficient specific conditions expressed in terms of linear matrix inequality (LMI) using the Lyapunov method to establish the asymptotic stability of solutions. Secondly, we use the differential transform method (DTM) to show numerical solutions. Finally, two examples are presented to demonstrate the effectiveness and applicability of proposed methods by Matlab and an appropriate computer program. © 2021, Bayram Sahin. All rights reserved.