Browsing by Author "Tunç, C."

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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.
An Analysis on the Weighted Pseudo Almost Periodic Solutions of Hornns With Variable Delays
(Palestine Polytechnic University, 2023) Yazgan, R.; Tunç, C.
This study belongs to a class of high order recurrent neural networks differential equations with variable delays. With the help of theory of weighted pseudo almost peri-odic(WPAP) functions and some differential inequalities, we investigate the existence of the solutions of the considered model and the exponential stability of these solutions. An example is given as an application of these results. © Palestine Polytechnic University-PPU 2023.
Bounded Solutions To Nonlinear Delay Differential Equations of Third Order
(Juliusz Schauder Center for Nonlinear Studies, 2009) Tunç, C.
This paper gives some sufficient conditions for every solution of delay differential equation ẍ̇ (t) + f(t, x(t), x(t - r), ẋ (t), ẋ (t - r), ẍ(t), ẍ(t - r)) + b(t)g(x(t - r), ẋ (t - r)) + c(t)h(x(t)) = p(t, x(t), x(t - r), ẋ (t), ẋ (t - r), ẍ(t)) to be bounded. © 2009 Juliusz Schauder Center for Nonlinear Studies.
Boundedness and Square Integrability of Solutions of Nonlinear Fourth-Order Differential Equations With Bounded Delay
(Texas State University - San Marcos, 2017) Korkmaz, E.; Tunç, C.
In this article, we give sufficient conditions for the boundedness, uniformly asymptotic stability and square integrability of the solutions to a fourth-order non-autonomous differential equation with bounded delay by using Lyapunov’s second method. © 2017 Texas State University.
Boundedness of Solutions of a Third-Order Nonlinear Differential Equation
(2005) Tunç, C.
Sufficient conditions are established for the boundedness of all solutions of (1.1), and we also present some sufficient conditions, which ensure that the limits of first and second order derivatives of the solutions of (1.1) tend to zero as t → ∞. Our results improve and include those results obtained by previous authors ([3], [5]).
The Boundedness of Solutions To Nonlinear Third Order Differential Equations
(2010) Tunç, C.
Abstract: In this paper, we establish some new sufficient conditions under which all solutions of nonlinear third order differential equations of the form x‴ + ip(x, x′)x″ + f(x, x′) = p(t, x, x, x″) are bounded. For illustrations, an example is also given on the bounded solutions. © 2010 InforMath Publishing Group.
Continuability and Boundedness of Solutions for a Kind of Nonlinear Delay Integrodifferential Equations of the Third Order
(Springer New York LLC, 2019) Tunç, C.; Ayhan, T.
In the paper, we consider a nonlinear integrodifferential equation of the third order with delay. We establish sufficient conditions guaranteeing the global existence and boundedness of the solutions of the analyzed equation. We use the Lyapunov second method to prove the main result. An example is also given to illustrate the applicability of our result. The result of this paper is new and improves previously known results. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.
Dynamics of an Arbitrary Order Model of Toxoplasmosis Ailment in Human and Cat Inhabitants
(Taylor and Francis Ltd., 2021) Zafar, Z.U.A.; Tunç, C.; Ali, N.; Zaman, G.; Thounthong, P.
In this article, a non-integer nonlinear mathematical model for toxoplasmosis disease in human and cat population is proposed and studied. The basic concepts of the model's dynamic are given. The study of qualitative dynamics is done by the basic threshold parameter (Formula presented.). Local and global stabilities are done and the system's disease free equilibrium point is an attractor when (Formula presented.). Besides of it, endemic equilibrium point is an attractor when (Formula presented.). The sensitivity analysis of (Formula presented.) shows which parameter has positive/negative impact on the model. Numerical simulation of the model for the parameters occurred in threshold parameter is also discussed. The techniques of Adams Bashforth Moulton will be considered to justify all the derived theoretical results which will help in understanding to study the effect of various parameters to both the transient and steady-state dynamics of the disease infection. © 2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
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
Exploring the Lower and Upper Solutions Approach for Abc-Fractional Derivative Differential Equations
(Springer, 2024) Talib, I.; Riaz, M.B.; Batool, A.; Tunç, C.
The lower and upper solution approach has been widely employed in the literature to ensure the existence of solutions for integer-order boundary value problems. Therefore, in this proposed study, our primary objective is to extend this method to establish the existence results for Atangna-Baleanu-Caputo (ABC) fractional differential equations of order 0<γ<1, with generalized nonlinear boundary conditions. We propose a generalized approach that unifies the existence criteria for certain specific boundary value problems formulated using the ABC fractional-order derivative operator, particularly addressing periodic and anti-periodic cases as special instances. The framework of the proposed generalized approach relies heavily on the concept of coupled lower and upper solutions together with certain fixed point results, including Arzela-Ascoli and Schauder’s fixed point theorems. By means of the generalized approach, we first define appropriate lower and upper solutions that bound the potential solution. We then construct a modified problem that incorporates these bounding solutions, ensuring the existence of a solution to the original problems without relying on iterative techniques. This approach involves verifying that the lower solution is less than or equal to the upper solution, and that both satisfy the given boundary conditions, thus guaranteeing the existence of a solution within the specified bounds. The inclusion of the specific examples with periodic and anti-periodic boundary conditions further reinforces the validity and relevance of our theoretical results. © The Author(s), under exclusive licence to Springer Nature India Private Limited 2024.
Extension of Lower and Upper Solutions Approach for Generalized Nonlinear Fractional Boundary Value Problems
(Taylor and Francis Ltd., 2022) Batool, A.; Talib, I.; Riaz, M.B.; Tunç, C.
Our main concern in this study is to present the generalized results to investigate the existence of solutions to nonlinear fractional boundary value problems (FBVPs) with generalized nonlinear boundary conditions. The framework of the presented results relies on the lower and upper solutions approach which allows us to ensure the existence of solutions in a sector defined by well-ordered coupled lower and upper solutions. It is worth mentioning that the presented results unify the existence criteria of certain problems which were treated on a case-by-case basis in the literature. Two examples are supplied to support the results. © 2022 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the University of Bahrain.
Fuzzy Fixed Point Results Via Rational Type Contractions Involving Control Functions in Complex-Valued Metric Spaces
(Natural Sciences Publishing, 2018) Humaira,; Sarwar, M.; Tunç, C.
In this work, we have proved some common fuzzy fixed point results satisfying rational contractive condition in the consideration of different types of control function used as coefficients in contractive condition. The results in this paper generalizes some results already proved in literature. Examples are given in the support of our constructed results. © 2018 NSP.
Gaps Between Zeros of Solutions for a Certain Class of Third-Order Differential Equations
(Taylor and Francis Ltd., 2019) Arahet, M.A.; Saker, S.H.; Tunç, C.
In this paper, we establish some lower bounds for the distance between zeros of nontrivial solutions or/and their derivatives and extend some results about distribution of zeros for a certain class of third-order differential equations of the form (Formula presented.) The main results of this paper will be proved by employing some Hardy’s and Opial’s type inequalities. © 2019, © 2019 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the University of Bahrain.
General Decay Stability of Nonlinear Delayed Hybrid Stochastic System With Switched Noises
(Biemdas Academic Publishers, 2024) Zouine, A.; Imzegouan, C.; Bouzahir, H.; Tunç, C.
Hybrid stochastic differential equations (HSDEs) have wide range of real-world applications. In this paper, we study a new kind of nonlinear delayed neutral stochastic differential equations with Markovian switched noises (NHSDE-MSN). Under the assumption that this type of equations satisfies the locally Lipschitz condition and general condition of monotonicity, the existence and uniqueness of global solutions are established. Then, based on the Lyapunov function, M-matrix theory, stochastic analysis techniques, and Barbalat lemma, taking into account the delay as a bounded function, different decay stabilities of solutions are investigated. Finally, a numerical example is given to illustrate the utility of the main results. © 2024 Biemdas Academic Publishers. All rights reserved.
Heat Transfer and Flow of Mhd Micropolarnanofluid Through the Porous Walls, Magnetic Fields and Thermal Radiaton
(Palestine Polytechnic University, 2022) Akinshilo, A.T.; Davodi, A.G.; Rezazadeh, H.; Sobamowo, G.; Tunç, C.
The analytical study of heat transfer and on the other hand flow of MHD micropolar nano fluid, which is affected by thermal radiation in a magneto porous wall channel, is presented. Equations governing the momentum and energy mechanics are transformed to differentials of nonlinear ordinary equations with the appropriate boundary conditions adopting the similarity transformation technique. The differentials of non-linear ordinary equations (ODE) are solved analytically using HPM method. Several significant parameters such as the nano fluid concentration, the micro-polar parameter, the radiation parameter on the temperature and velocity profiles and magnetic parameter are investigated. Moreover, figures illustrate what the actual Nusselt number is. © Palestine Polytechnic University-PPU 2022.
Instability for Nonlinear Differential Equations of Fifth Order Subject To Delay
(2012) Tunç, C.
This paper studies the instability of zero solution of a certain fifth order nonlinear delay differential equation. Sufficient conditions for the instability of zero solution of the equation considered are obtained by the Lyapunov-Krasovskii functional approach. © 2012 InforMath Publishing Group.
Instability of a Fifth-Order Nonlinear Vector Delay Differential Equation With Multiple Deviating Arguments
(Hindawi Publishing Corporation, 2013) Tunç, C.
We study a fifth-order nonlinear vector delay differential equation with multiple deviating arguments. Some criteria for guaranteeing the instability of zero solution of the equation are given by using the Lyapunov-Krasovskii functional approach. Comparing with the previous literature, our result is new and complements some known results. © 2013 Cemil Tunç.
Instability of Solutions for Nonlinear Functional Differential Equations of Fifth Order With N-Deviating Arguments
(2012) Tunç, C.
In this paper, we study the instability properties of solutions of a class of nonlinear functional differential equations of the fifth order with n-constant deviating arguments. By using the Lyapunov-Krasovskii functional approach, we obtain some interesting sufficient conditions ensuring that the zero solution of the equations is unstable. © Cemil Tunç, 2012.
Lower and Upper Bounds for the Blow Up Time for Generalized Heat Equations With Variable Exponents
(Palestine Polytechnic University, 2021) Pişkin, E.; Dinç, Y.; Tunç, C.
This paper deals with the initial-boundary value problem for generalized heat equations with variable exponent in a bounded domain. Under suitable conditions, we discuss the lower and upper bounds for the blow up time of solutions. © Palestine Polytechnic University-PPU 2021.
A New Boundedness Result To Nonlinear Differential Equations of Third Order With Finite Lag
(2009) Tunç, C.
Criteria for boundedness of solutions to the nonlinear third order delay differential (mathematical equation is )p(x{t),x'(t),x"{t))x"(t) + ip{x{t - r(t)),x'(t-r{t))) + h{x{t - r{t))) = p(i, x{t), x(t - r(t)), x'{t), x'(t - r(t)), x"(t)) are obtained by Lyapunov's second method. By introducing a Lyapunov functional, sufficient conditions are established that guarantee that all solutions of this equation are bounded. An example is also given to illustrate the importance of result obtained. Our findings improve a result existing in the literature to boundedness of solutions for this delay differential equation. © Dynamic Publishers, Inc.