Browsing by Author "Tunc, Cemil"

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About Uniform Boundedness and Convergence of Solutions of Certain Non-Linear Differential Equations of Fifth-Order
(Malaysian Mathematical Sciences Soc, 2007) Tunc, Cemil
In this paper, we establish sufficient conditions under which all solutions of equation of the type X-(5) + f (t, (x)over dot, (x)double over dot, (x) triple over dot, x((4))) + phi(t, (x)over dot, <(x)double over dot>, (x) triple over dot) + phi (t, x, (x)over dot, <(x)double over dot>) + g(t, x, (x)over dot) + e(t)h(x) = p(t, x, (x)over dot, <(x)double over dot>, (x) triple over dot, x((4))) are uniformly bounded and tend to zero as t -> infinity. Our theorem is stated in a more general form; it extends some related results known in the literature. Also, the relevance of our result is to show that the results established in Abou El-Ela and Sadek [2,3] and Sadek [13] contain some superfluous conditions.
Advancing Computation in Solving Non-Homogeneous Parabolic Problem With Non-Linear Integral Boundary Conditions Via the Cubic B-Spline Method
(Yokohama Publ, 2025) Redouane, Kelthoum Lina; Arar, Nouria; Tunc, Cemil
The aim of this research is to improve the cubic B-spline method for finding the approximate solution of one-dimensional non-homogeneous reaction-diffusion equation with non-linear integral boundary conditions. In this work, an approximate solution is built by combining a Crank-Nicolson scheme for temporal discretization and a modified cubic B-spline basis with a new i coefficient. This n coefficient is chosen to ensure the suggested technique's convergence to enhance the efficiency of the existing cubic B-spline techniques. Thus, the numerical method employed for dealing with the integral non-linear boundary conditions produces a system that possesses a tridiagonal coefficient matrix, except for the first and last lines. Furthermore, a predictor-corrector approach for solving the resultant non-linear system due to the integral and non-linear boundary conditions is presented as well as some convergence results are then updated numerically. The novelty and originality of this article are that the considered non-linear integral boundary conditions are new conditions of mathematical models as well as the modified basis given in this paper and the outcomes are also new. Finally, the robustness and efficiency of our approach are demonstrated by testing our technique on three examples with integral boundary conditions of order c = 2. Our findings have been shown to be more accurate and to offer challenging upgrades over those found in the literature.
Analogues To Lie Method and Noether's Theorem in Fractal Calculus
(Mdpi, 2019) Golmankhaneh, Alireza Khalili; Tunc, Cemil
In this manuscript, we study symmetries of fractal differential equations. We show that using symmetry properties, one of the solutions can map to another solution. We obtain canonical coordinate systems for differential equations on fractal sets, which makes them simpler to solve. An analogue for Noether's Theorem on fractal sets is given, and a corresponding conservative quantity is suggested. Several examples are solved to illustrate the results.
Analysis and Numerical Simulation of Tuberculosis Model Using Different
(Pergamon-elsevier Science Ltd, 2022) Zafar, Zain Ul Abadin; Zaib, Sumera; Hussain, Muhammad Tanveer; Tunc, Cemil; Javeed, Shumaila
The main goal of the current research is to study and explore dynamic behavior of tuberculosis by using fractional mathematical model. In this study, recently introduced fractional operator (FO) having ML non-singular kernel was used. Fixed point theory is utilized to explore the unique and existing problems in suitable model. Numerical outcomes are discovered for the verification of arbitrary fractional order derivative. These numerical outcomes are discovered from mathematical and biological perspectives by using the model parameters values. Graphical simulation shows the comparison between Fractional Caputo (Fr. Cap) method and AB Caputo (AB Cap) predictor corrector method for different fraction order. The present study suggested that AB Cap is much better than Fr. Cap.(c) 2022 Elsevier Ltd. All rights reserved.
Analysis and Numerical Simulations of Fractional Order Vallis System
(Elsevier, 2020) Zafar, Zain Ul Abadin; Ali, Nigar; Zaman, Gul; Thounthong, Phatiphat; Tunc, Cemil
This paper represents a non-integer-order Vallis systems in which we applied the Gru & uml; nwald-Letnikov tactics with Binomial coefficients in order to realize the numerical simulations to a set of equations. Recently researchers reported in the literature that it is the generalization of integer order dynamical model. Several cases involving non-integer and integer analysis with differ-ent values of non-integer order have been applied to Vallis systems to see the behavior of simula-tions. To visualize the effect of non-integer order approach, the time histories and phase portraits have been plotted. The consequences expose that the non-integer-order Vallis model can reveal a genuine equitable comportment to Vallis systems and might bid greater perceptions towards the understanding of such complex dynamic systems (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
Analysis of Efficient Discretization Technique for Nonlinear Integral Equations of Hammerstein Type
(Emerald Group Publishing Ltd, 2024) Bhat, Imtiyaz Ahmad; Mishra, Lakshmi Narayan; Mishra, Vishnu Narayan; Tunc, Cemil
PurposeThis study focuses on investigating the numerical solution of second-kind nonlinear Volterra-Fredholm-Hammerstein integral equations (NVFHIEs) by discretization technique. The purpose of this paper is to develop an efficient and accurate method for solving NVFHIEs, which are crucial for modeling systems with memory and cumulative effects, integrating past and present influences with nonlinear interactions. They are widely applied in control theory, population dynamics and physics. These equations are essential for solving complex real-world problems.Design/methodology/approachDemonstrating the solution's existence and uniqueness in the equation is accomplished by using the Picard iterative method as a key technique. Using the trapezoidal discretization method is the chosen approach for numerically approximating the solution, yielding a nonlinear system of algebraic equations. The trapezoidal method (TM) exhibits quadratic convergence to the solution, supported by the application of a discrete Gr & ouml;nwall inequality. A novel Gr & ouml;nwall inequality is introduced to demonstrate the convergence of the considered method. This approach enables a detailed analysis of the equation's behavior and facilitates the development of a robust solution method.FindingsThe numerical results conclusively show that the proposed method is highly efficacious in solving NVFHIEs, significantly reducing computational effort. Numerical examples and comparisons underscore the method's practicality, effectiveness and reliability, confirming its outstanding performance compared to the referenced method.Originality/valueUnlike existing approaches that rely on a combination of methods to tackle different aspects of the complex problems, especially nonlinear integral equations, the current approach presents a significant single-method solution, providing a comprehensive approach to solving the entire problem. Furthermore, the present work introduces the first numerical approaches for the considered integral equation, which has not been previously explored in the existing literature. To the best of the authors' knowledge, the work is the first to address this equation, providing a foundational contribution for future research and applications. This innovative strategy not only simplifies the computational process but also offers a more comprehensive understanding of the problem's dynamics.
An Analysis on the Periodic Solutions of An N-Th Order Non-Linear Differential Equation
(Univ Prishtines, 2021) Yazgan, Ramazan; Tunc, Cemil
This paper deals with existence of w-periodic solutions of a nonlinear n-th order differential equation with variable delays. Some sufficient conditions related to w-periodicity of solutions were obtained by using coincidence degree theory. In a particular case, an application showing the accuracy of our results was given.
An Analytical Method for Solving Exact Solutions of the Nonlinear Bogoyavlenskii Equation and the Nonlinear Diffusive Predator-Prey System
(Elsevier Science Bv, 2016) Alam, Md. Nur; Tunc, Cemil
In this article, we apply the exp(-Phi(xi))-expansion method to construct many families of exact solutions of nonlinear evolution equations (NLEEs) via the nonlinear diffusive predator-prey system and the Bogoyavlenskii equations. These equations can be transformed to nonlinear ordinary differential equations. As a result, some new exact solutions are obtained through the hyperbolic function, the trigonometric function, the exponential functions and the rational forms. If the parameters take specific values, then the solitary waves are derived from the traveling waves. Also, we draw 2D and 3D graphics of exact solutions for the special diffusive predator-prey system and the Bogoyavlenskii equations by the help of programming language Maple. (C) 2016 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
An Analytical Technique for Solving New Computational Solutions of the Modified Zakharov-Kuznetsov Equation Arising in Electrical Engineering
(Shahid Chamran Univ Ahvaz, Iran, 2021) Islam, Shariful; Alam, Md Nur; Fayz-Al-Asad, Md; Tunc, Cemil
The modified (G'/G)-expansion method is an efficient method that has appeared in recent times for solving new computational solutions of nonlinear partial differential equations (NPDEs) arising in electrical engineering. This research has applied this process to seek novel computational results of the developed Zakharov-Kuznetsov (ZK) equation in electrical engineering. With 3D and contour graphical illustration, mathematical results explicitly exhibit the proposed algorithm's complete honesty and high performance.
Analyzing the Stability of Fractal Delay Differential Equations
(Pergamon-elsevier Science Ltd, 2024) Golmankhaneh, Alireza Khalili; Tunc, Cemil
In this paper, we provide a comprehensive overview of fractal calculus and investigate the stability of both linear and non-linear fractal delay differential equations with fractal support. Our analysis encompasses the stability of the fractal Mackey-Glass equation as well as fractal differential equations with single and dual delays. Additionally, we introduce a predictor-corrector scheme to solve the fractal one-delay differential equation. Several examples are presented to illustrate the effects of fractal-order differentiation, which arise from the dimensionality of the fractal support, and the impact of fractal delays.
An Application of Lyapunov Functions To Properties of Solutions of a Perturbed Fractional Differential System
(Lebanese Univ, 2022) Tunc, Cemil
This paper deals with a perturbed nonlinear system of fractional order differential equations (FrODEs) with Caputo derivative. The purpose of the paper is to discuss uniform stability (US), asymptotic stability (AS), Mittag-Leffer stability (MLS) of zero solution and boundedness at infinity of non-zero solutions of this perturbed nonlinear system of FrODEs with Caputo derivative. We obtain four new theorems on these mathematical concepts via a Lyapunov function (LF) and its Caputo derivative. For illustration, an example is provided which satisfies assumptions of the four new results and, in particular, shows their applications. The new results of this paper generalize and improve some recent ones in the literature and they have contributions to theory of FrODEs.
Application of Variation of Parameter's Method for Hydrothermal Analysis on Mhd Squeezing Nanofluid Flow in Parallel Plates
(Univ Tabriz, 2022) Zabihi, Ali; Akinshilo, Akinbowale T.; Rezazadeh, Hadi; Ansari, Reza; Sobamowo, M. Gbeminiyi; Tunc, Cemil
In this paper, the transport of flow and heat transfer through parallel plates arranged horizontally against each other is studied. The mechanics of fluid transport and heat transfer are formulated utilizing systems of the coupled higher-order numerical model. This governing transport model is investigated by applying the variation of the parameter's method. Result obtained from the analytical study is reported graphically. It is observed from the generated result that the velocity profile and thermal profile drop by increasing the squeeze parameter. The drop inflow is due to limitations in velocity as plates are close to each other. Also, thermal transfer due to flow pattern causes decreasing boundary layer thickness at the thermal layer, consequently drop in thermal profile. The analytical obtained result from this study is compared with the study in literature for simplified cases, this shows good agreement. The obtained results may therefore provide useful insight to practical applications including food processing, lubrication, and polymer processing industries amongst other relevant applications.
Approximate Analytical Solutions of Space-Fractional Telegraph Equations by Sumudu Adomian Decomposition Method
(Prairie View A & M Univ, dept Mathematics, 2018) Khan, Hasib; Tunc, Cemil; Khan, Rahmat Ali; Shirzoi, Akhtyar Gul; Khan, Aziz
The main goal in this work is to establish a new and efficient analytical scheme for space fractional telegraph equation (FTE) by means of fractional Sumudu decomposition method (SDM). The fractional SDM gives us an approximate convergent series solution. The stability of the analytical scheme is also studied. The approximate solutions obtained by SDM show that the approach is easy to implement and computationally very much attractive. Further, some numerical examples are presented to illustrate the accuracy and stability for linear and nonlinear cases.
Asymptotic Behavior of Levin-Nohel Nonlinear Difference System With Several Delays
(Amer inst Mathematical Sciences-aims, 2024) Mesmouli, Mouataz Billah; Tunc, Cemil; Hassan, Taher S.; Zaidi, Hasan Nihal; Attiya, Adel A.
In this manuscript, we considered a system of difference equations with delays and we established sufficient conditions to guarantee stability, asymptotic stability and exponential stability. In each type of stability, we created an appropriate space that guarantees us the existence of a fixed point that achieves the required stability.
Asymptotic Stability and Boundedness Criteria for Nonlinear Retarded Volterra Integro-Differential Equations
(Elsevier, 2018) Tunc, Cemil
In this article, we construct new specific conditions for the asymptotic stability (AS) and boundedness (B) of solutions to nonlinear Volterra integro-differential equations (VIDEs) of first order with a constant retardation. Our analysis is based on the successful construction of suitable Lyapunov-Krasovskii functionals (LKFs). The results of this paper are new, and they improve and complete that can be found in the literature. (C) 2017 The Author. Production and hosting by Elsevier B.V. on behalf of King Saud University.
Asymptotic Stability in Neutral Differential Equations With Multiple Delays
(Univ Prishtines, 2016) Tunc, Cemil; Altun, Yener
The aim of this paper is to investigate the asymptotic stability of solutions to certain neutral functional differential equations of first order. We obtain specific sufficient conditions expressed in terms of matrix inequality to verify the asymptotic stability of solutions. The technique of proof involves a functional method. We also give an example to illustrate the feasibility and correctness of the main result by MATLAB-Simulink. Our result has a contribution to the literature.
Asymptotic Stability of Solutions for a Kind of Third-Order Stochastic Differential Equations With Delays
(Univ Miskolc inst Math, 2019) Mahmoud, Ayman M.; Tunc, Cemil
This work is devoted to investigate the stochastic asymptotically stability of the zero solution for a kind of third-order stochastic differentials equation with variable and constant delays by a suitable Lyapunov functional. Our results improve and form a complement to some results that can be found in the literature. In the last section, we give an example to illustrate our main result.
Asymptotic Stability of Solutions of a Class of Neutral Differential Equations With Multiple Deviating Arguments
(Soc Matematice Romania, 2014) Tunc, Cemil
In this paper, using the Lyapunov-Krasovskii functional approach, some novel stability criteria are presented for all solutions of a class of nonlinear neutral differential equations to tend zero when t -> infinity.
Asymptotically Linear Solutions of Differential Equations Via Lyapunov Functions
(Elsevier Science inc, 2009) Mustafa, Octavian G.; Tunc, Cemil
We discuss the existence of solutions with oblique asymptotes to a class of second order nonlinear ordinary differential equations by means of Lyapunov functions. The approach is new in this field and allows for simpler proofs of general results regarding Emden-Fowler like equations. (C) 2009 Elsevier Inc. All rights reserved.
B-Spline Curve Theory: an Overview and Applications in Real Life
(de Gruyter Poland Sp Z O O, 2024) Hasan, Md. Shahid; Alam, Md. Nur; Fayz-Al-Asad, Md.; Muhammad, Noor; Tunc, Cemil
This study commences by delving into B-spline curves, their essential properties, and their practical implementations in the real world. It also examines the role of knot vectors, control points, and de Boor's algorithm in creating an elegant and seamless curve. Beginning with an overview of B-spline curve theory, we delve into the necessary properties that make these curves unique. We explore their local control, smoothness, and versatility, making them well-suited for a wide range of applications. Furthermore, we examine some basic applications of B-spline curves, from designing elegant automotive curves to animating lifelike characters in the entertainment industry, making a significant impact. Utilizing the de Boor algorithm, we intricately shape the contours of everyday essentials by applying a series of control points in combination with a B-spline curve. In addition, we offer valuable insights into the diverse applications of B-spline curves in computer graphics, toy design, the electronics industry, architecture, manufacturing, and various engineering sectors. We highlight their practical utility in manipulating the shape and behavior of the curve, serving as a bridge between theory and application.