Browsing by Author "Tunc, C."

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Applications of Delay Differential Equations in Biological Systems
(Wiley-hindawi, 2018) Rihan, F. A.; Tunc, C.; Saker, S. H.; Lakshmanan, S.; Rakkiyappan, R.
Coupled Lower and Upper Solution Approach for the Existence of Solutions of Nonlinear Coupled System With Nonlinear Coupled Boundary Conditions
(Universidad Catolica del Norte, 2016) Talib, I.; Asif, N.A.; Tunc, C.
The present article investigates the existence of solutions of the following nonlinear second order coupled system with nonlinear coupled boundary conditions (CBCs), where f1, f2: [0, 1] × R → R, μ: R6 → R2 and v: R2 → R2 are continuous functions. The results presented in [γ, 11] are extended in our article. Coupled lower and upper solutions, Arzela-Ascoli theorem and Schauder's fixed point theorem play an important role in establishing the arguments. Some examples are taken to ensure the validity of the theoretical results.
Covering Properties by (a)-Θ Sets in (A)topological Spaces
(Palestine Polytechnic University, 2022) Luthra, S.; Chauhan, H.V.S.; Tyagi, B.K.; Tunc, C.
We introduced the concept of (a)-θ-compactness and (a)-θ-Mengerness in (a)topological spaces. We discussed the relationship of the above notions with the other known covering properties. It is shown that the product of two (a)-θ-Menger (resp. (a)-θ-compact) spaces is (a)-θ-Menger (resp. (a)-θ-compact) if one of them is (a)s-compact. If Xi is (a)-θ-Menger for each finite i, then (a)topological space X satisfies the selection principle Sfin(Θ-Ω(X ), Θ-Ω(X)). Further, it is shown that the (a)-θ-Menger covering property is preserved under (a)-θ-continuous and (a)-strongly-θ-continuous map. © Palestine Polytechnic University-PPU 2022.
Further Results on the Instability of Solutions of Certain Nonlinear Vector Differential Equations of Fifth Order
(Dixie W Publ Corp, 2008) Tunc, C.
By using Lyapunov's second method [13], some new results are established, which insure that the zero solution of non-linear vector differential equations of the form X((5)) + Psi((X) over dot, (X) doubt over dot) (X)triple over dot> + Phi(X, (X) over dot, (X) doubtle over dotm (X) triple over dot, X((4))) + Theta((X) over dot) + F(X) = 0 is unstable.
Global Existence and Boundedness on a Certain Nonlinear Integro-Differential Equation of Second Order
(Watam Press, 2017) Tunc, C.; Ahyan, T.
In this paper, we give new criteria for global existence and boundedness of solutions on a certain nonlinear integro-differential equation of second order. The technique of the proof is based on an appropriate Lyapunov function. We provide a numerical example to confirm the effectiveness of the theoretical result. Our result extends and improves the results obtained by Napoles Valdes [13]. Copyright ©2017 Watam Press.
Implementation of Soliton Solutions for Generalized Nonlinear Schrodinger Equation With Variable Coefficients
(Cambridge Scientific Publishers, 2022) Rezazadeh, H.; Sab’u, J.; Zabihi, A.; Ansari, R.; Tunc, C.
This article deals with new soliton solutions of the generalized nonlinear Schrödinger equation with variable coefficients by the direct algebraic method. Once the variables of this technique are considered as special values, we could achieve the solitary waves that are unique from those attained by the other methods. It can be inferred that the solution methodology in conjunction with symbolic computing eligible to solve nonlinear partial differential equations precisely. © CSP - Cambridge, UK; I&S - Florida, USA, 2022
Instability of Solutions for Certain Nonlinear Vector Differential Equations of Fourth Order
(Springer, 2009) Tunc, C.
The main purpose of this paper is to give a result with explanatory example that deals directly with the instability of the trivial solution of a certain nonlinear vector differential equation of the fourth order. The result established here improves and includes a well-known instability result established for a scalar nonlinear differential equation of the fourth order.
New Carlson-Bellman and Hardy-Littlewood Dynamic Inequalities
(Element, 2018) Saker, S. H.; Tunc, C.; Mahmoud, R. R.
In this paper, we will prove some new dynamic inequalities of Carlson and Hardy-Littlewood types on an arbitrary time scale T. These inequalities as special cases contain the classical continuous and discrete Carlson-Bellman and Hardy-Littlewood type inequalities. The results will be proved by employing the time scales Holder inequality, some algebraic inequalities and some basic lemmas designed and proved for this purpose.
New Generalizations of Nemethmohapatra Type Inequalities on Time Scales
(Springer, 2017) Agarwal, R. P.; Mahmoud, R. R.; Saker, S. H.; Tunc, C.
Some new dynamic inequalities on time scales are established, that reduce in the discrete and the continuous cases to classical inequalities named after Nemeth and Mohapatra, respectively. The new generalized inequalities resemble intensive classical inequalities known in the literature such as Beesack type inequalities, Copson type inequalities and Hardy-Littlewood type inequalities. The main results will be proved by employing the time scales Holder inequality and the time scales power rules for integrations that have been proved earlier.
Nonlinear Fractional Partial Coupled Systems Approximate Solutions Through Operational Matrices Approach
(Cambridge Scientific Publishers, 2019) Talib, I.; Belgacem, F.B.M.; Khalil, H.; Tunc, C.
In this article, the numerical method based on operational matrices of fractional order derivatives and integrals in the Caputo and Riemann-Liouville senses of two-parametric orthogonal shifted Jacobi polynomials is proposed for studying the approximate solutions for a generalized class of fractional order partial differential equations. The technique is extended herein to generalized classes of fractional order coupled systems having mixed partial derivatives terms. One salient aspect of this article is the development of a new operational matrix for mixed partial derivatives in the sense of Caputo. Validity of the method is established by comparing our simulated results with literature solutions obtained otherwise, yielding negligible errors. Furthermore, as a result of the comparative study, some results presented in the literature are extended and improved in the investigation herein. © 2019, Cambridge Scientific Publishers.
A Note on the Exponential Stability of Linear Systems With Variable Retardations
(Natural Sciences Publishing USA, 2017) Gözen, M.; Tunc, C.
We here investigate the exponential stability of a kind of linear systems of first order with variable delay. By means of an auxiliary functional, we discuss exponential stability of solutions of the system considered. During the proof, we also benefit from linear matrix inequalities (LMIs). © 2017. NSP Natural Sciences Publishing Cor.
Numerical Simulations of the Fractional-Order Siq Mathematical Model of Corona Virus Disease Using the Nonstandard Finite Difference Scheme
(Univ Putra Malaysia Press, 2022) Raza, N.; Bakar, A.; Khan, A.; Tunc, C.
This paper proposes a novel nonlinear fractional-order pandemic model with Caputo derivative for corona virus disease. A nonstandard finite difference (NSFD) approach is presented to solve this model numerically. This strategy preserves some of the most significant physical properties of the solution such as non-negativity, boundedness and stability or convergence to a stable steady state. The equilibrium points of the model are analyzed and it is determined that the proposed fractional model is locally asymptotically stable at these points. Non-negativity and boundedness of the solution are proved for the considered model. Fixed point theory is employed for the existence and uniqueness of the solution. The basic reproduction number is computed to investigate the dynamics of corona virus disease. It is worth mentioning that the non-integer derivative gives significantly more insight into the dynamic complexity of the corona model. The suggested technique produces dynamically consistent outcomes and excellently matches the analyticalworks. To illustrate our results, we conduct a comprehensive quantitative study of the proposed model at various quarantine levels. Numerical simulations show that can eradicate a pandemic quickly if a human population implements obligatory quarantine measures at varying coverage levels while maintaining sufficient knowledge.
On Existence of Periodic Solution To Certain Nonlinear Third Order Differential Equations
(Universidad Catolica del Norte, 2009) Tunc, C.
In this paper, it is investigated the existence of periodic solutions to the nonlinear third order differential equation: x‴ + c2(t)x″ + c1(f)x′ + f(t, x) = p(t, x, x′, x″). The Leray-Schauder principle is used to show the existence of periodic solutions of this equation.
On Qualitative Behaviors of Nonlinear Singular Systems With Multiple Constant Delays
(Islamic Azad Univ, Shiraz Branch, 2022) Yigit, A.; Tunc, C.
In this paper, we investigate some qualitative properties of a class of nonlinear singular systems with multiple constant delays. By using the Lyapunov-Krasovskii functional (LKF) method and integral inequalities, we obtain some new sufficient conditions which guarantee that the considered systems are regular, impulse-free and exponentially stable. Two numerical examples are provided to illustrate the application of the obtained results using MATLAB software. By this paper, we extend and improve some results in the literature.
On System of Nonlinear Coupled Differential Equations and Inclusions Involving Caputo-Type Sequential Derivatives of Fractional Order
(Taylor & Francis Ltd, 2022) Subramanian, M.; Manigandan, M.; Tunc, C.; Gopal, T. N.; Alzabut, J.
We investigate a new class of boundary value problems of a nonlinear coupled system of sequential fractional differential equations and inclusions involving Caputo fractional derivatives and boundary conditions. We use standard fixed-point theory tools to deduce sufficient criteria for the existence and uniqueness of solutions to the problems at hand. Examples are discussed to illustrate the validity of the proposed results.
On the Asymptotic Stability, Uniform Stability, and Boundedness of Solutions To Nonlinear Volterra Integrodifferential Equations
(Springer, 2021) Tunc, C.; Mohammed, S. A.
We present the definitions of two new Lyapunov functionals. These functionals are applied to establish sufficient conditions guaranteeing the asymptotic stability, uniform stability, and boundedness of solutions of certain nonlinear Volterra integrodifferential equations of the first order. The obtained results improve and extend known results available from literature. We also propose examples to show the applicability of our results and illustrate them. By using MATLAB-Simulink, we clearly show, in particular cases, the behavior of orbits of the analyzed Volterra integrodifferential equations.
On the Convergence of Solutions of Some Nonlinear Differential Equations of Fourth Order
(InforMath Publishing Group, 2014) Korkmaz, E.; Tunc, C.
In this paper, we consider a nonlinear differential equation of fourth order. By the Lyapunov function approach, we discuss the convergence of the solutions of the equation considered. Our findings generalize some well known results in the literature. © 2014 InforMath Publishing Group.
On the New Qualitative Results in Integro-Differential Equations With Caputo Fractional Derivative and Multiple Kernels and Delays
(Yokohama Publ, 2022) Tunc, C.; Tunc, O.; Yao, J. C.
In this paper, qualitative properties such as uniform stability (US), asymptotic stability (AS) and Mittag-Leffler stability (MLS) of trivial solution and boundedness of nonzero solutions of a system of non-linear fractional integrodelay differential equations (FFIDDEs) with Caputo fractional derivative, multiple kernels and multiple delays are investigated. Four new theorems including sufficient conditions are proved on these qualitative concepts of solutions. The established conditions depend upon the verification of the basic qualitative results of fractional calculus and our main results, which are proved via the Lyapunov-Razumikhin method (LRM). In the end, as numerical applications of the proved theorems, an example is given to demonstrate the effectiveness of the applied method and obtained results. Our results improve and generalize the known ones in this direction.
On the Qualitative Analyses of Nonlinear Delay Differential Equations of Third Order
(Cambridge Scientific Publishers, 2022) Erdur, S.; Tunc, C.
The authors of this paper examine uniformly asymptotically stability (UAS), uniformly boundedness (UB), ultimately uniformly boundedness (UUB) and existence of periodic solutions (EPSs) of certain nonlinear delay differential equations (DDEs) of third order with multiple constant delays. They prove two results and give a corollary on these properties of solutions. The main results of this paper have sufficient conditions and the technique of the proofs for these results is based on construction of a proper Lyapunov-Krasovskiǐ function (LKF). This paper has novel results to the theory of DDEs of third order and fills some gaps related to the mentioned concepts. © CSP - Cambridge, UK; I&S - Florida, USA, 2022
On the Stability of Solutions for Non-Autonomous Delay Differential Equations of Third-Order
(Shiraz Univ, 2008) Tunc, C.
Some sufficient conditions for uniform asymptotic stability of null solution to a certain nonlinear delay differential equation of third order are established. By introducing a Lyapunov functional, a new result is obtained which includes and improves some related results in literature.