Sürdürülebilir Kalkınma Amaçları
Yayınlar
- MakaleAçık Erişim2019Solving of Some Random Partial Differential Equations by Using Differential Transformation Method and Laplace- Padé Method
Merdan, Mehmet; Bekiryazıcı, Zafer; Kesemen, Tülay; Anaç, Halil
In this study, the solutions of random partial differential equations are examined. The parameters and the initialconditions of the random component partial differential equations are investigated with Beta distribution. A fewexamples are given to illustrate the efficiency of the solutions obtained with the random Differential TransformationMethod (rDTM). Functions for the expected values and the variances of the approximate analytical solutions of therandom equations are obtained. Random Differential Transformation Method is applied to examine the solutions ofthese partial differential equations and MAPLE software is used for the finding the solutions and drawing the figures.Also the Laplace- Padé Method is used to improve the convergence of the solutions. The results for the randomcomponent partial differential equations with Beta distribution are analysed to investigate effects of this distribution onthe results. Random characteristics of the equations are compared with the results of the deterministic partial differentialequations. The efficiency of the method for the random component partial differential equations is investigated bycomparing the formulas for the expected values and variances with results from the simulations of the randomequations.
- MakaleAçık Erişim2019Diferansiyel Dönüşüm Yöntemi İle Rastgele Kalp Atış Modelinin Analizi
Oral, Pınar; Merdan, Mehmet; Bekiryazıcı, Zafer
Bu çalışmada, rastgele Zeeman Kalpatış Modelinin incelenmesi için diferansiyel dönüşüm yöntemi kullanılmıştır. Modelin bazı parametreleri ve başlangıç koşulları sırasıyla Beta ve Normal dağılımlara sahip rastgele değişkenler olarak alınmıştır. Rastgele Zeeman Modelinin yaklaşık analitik çözümü elde edilmiş ve model bileşenlerinin beklenen değer ve varyansı elde edilmiştir. Beta ve normal olarak dağılmış rastgele etkiler altında, rastgele modellerin sonuçları karşılaştırılmış ve bu durumlar için elde edilen yaklaşık sayısal karakteristikler karşılaştırılmıştır. Elde edilen yaklaşık formüllere, yaklaşımların yakınsama aralığını artırmak için Laplace-Padé Metodu uygulanarak iyileştirilmiş çözümler bulunmuştur.
- MakaleYalnız künye2019GLOBAL STABILITY IN A PATHOGEN-SPECIFIC CD8 IMMUNE RESPONSE PREDICTION MODEL
Anaç, Halil; Merdan, Mehmet; Beki̇Ryazici, Zafer
In this study, a system of ordinary differential equations used for modeling pathogen-specific CD8 cell immune response is studied. The positivity and the limitation of the model solutions are proven. The equilibrium points in the cases with the presence and the absence of the pathogen are determined and their stabilities are investigated. Furthermore, the essential reproduction number is obtained for the system. The conditions of the reproduction number for the stability of the equilibrium are shown and numerical examples are given for supporting the analytical results.
- MakaleYalnız künye2019THE NEW SUMUDU TRANSFORM ITERATIVE METHOD FOR STUDYING THE RANDOM COMPONENT TIME-FRACTIONAL KLEIN-GORDON EQUATION
Merdan, Mehmet; Anaç, Halil; Kesemen, Tülay
In this study, the solutions of the random component time-fractional Klein-Gordon equation is obtained as approximately or exactly. The initial condition of this Klein-Gordon equation is studied by Gamma distribution. The fractional derivatives are defined in the Caputo sense. An example is shown to illustrate the influence of the solutions obtained by the new Sumudu transform iterative method (NSTIM). The expected value and variance of these solutions of this Klein-Gordon equation are obtained. The approximate analytical solution of this equation obtained by NSTIM and VIM are compared. NSTIM is applied to analyze the solution of this equation. Solution and figures are obtained by using MAPLE software. The formulas for the expected values and variances and results from the simulations of this Klein-Gordon equation are compared and the efficiency of this method is investigated.
- MakaleAçık Erişim2018ANALYZING THE DYNAMICS OF EBOLA TRANSMISSION WITH RANDOM EFFECTS
Merdan, Mehmet; Bekiryazici, Zafer; Kesemen, Tulay; Khaniyev, Tahir
In this study, a deterministic mathematical model of Ebola transmission is analyzed under random ef-fects. A recent compartmental model of Berge et al. incorporates both direct and indirect transmission in the model. We assume the parameters of this model are normally distributed random variables to investigate the random behavior of disease transmission. Random differential transformation method is used to obtain the ap-proximate expectation of disease recovery. Furthermore, the approximation for expected recovery is modified by using Laplace-Padé method. Comparison of results indicate that the Laplace-Padé modification provides a better approximation. We also interpret the long term random behavior of the disease dynamics using simulation results.
- BildiriYalnız künye2018Generalized beta parameters for a SVEIR-type random model of Polio transmission
Bekiryazici, Zafer; Merdan, Mehmet; Kesemen, Tulay; Tosun, M.
In this study, a SVEIR-type compartmental model of Poliomyelitis transmission is examined under random effects. We introduce Generalized Beta and normal distributed random parameters into the equation system to investigate the random dynamics of the disease. The approximate analytical solution of the model under random effects is obtained by using Random Differential Transformation Method (RDTM). Results from simulations and RDTM are analyzed to comment on the randomness of the compartments and disease transmission. It is seen that the random model successfully provides similar results that can be obtained through the deterministic model while providing additional information on the random behavior of the disease, such as the standard deviations and the variation coefficients.
- MakaleAçık Erişim2017Deterministic stability and random behavior of a Hepatitis C model
Merdan, Mehmet; Bekiryazici, Zafer; Kesemen, Tulay; Khaniyev, Tahir
The deterministic stability of a model of Hepatitis C which includes a term defining the effect of immune system is studied on both local and global scales. Random effect is added to the model to investigate the random behavior of the model. The numerical characteristics such as the expectation, variance and confidence interval are calculated for random effects with two different distributions from the results of numerical simulations. In addition, the compliance of the random behavior of the model and the deterministic stability results is examined.
- MakaleAçık Erişim2017Comparison of stochastic and random models for bacterial resistance
Merdan, Mehmet; Bekiryazici, Zafer; Kesemen, Tulay; Khaniyev, Tahir
In this study, a mathematical model of bacterial resistance considering the immune system response and antibiotic therapy is examined under random conditions. A random model consisting of random differential equations is obtained by using the existing deterministic model. Similarly, stochastic effect terms are added to the deterministic model to form a stochastic model consisting of stochastic differential equations. The results from the random and stochastic models are also compared with the results of the deterministic model to investigate the behavior of the model components under random conditions.
- MakaleAçık Erişim2016On the fractional Riccati differential equation
Khaniyev, Tahir; Merdan, Mehmet
In this paper, We tried to find an analytical solution of nonlinear Riccati conformable fractional differential equation. Fractional derivatives are described in the conformable derivative. The behavior of the solutions and the effects of different values of fractional order α are presented graphically and table. The results obtained by the CFD(conformable fractional derivative) are compared with homotopy perturbation method(HPM), fractional variational iteration method(FVIM).
- MakaleYalnız künye2015On the solutions of time-fractio3nal generalized hirota-satsuma coupled-KDV equation with modified riemann-liouville derivative by an analytical technique
Merdan, Mehmet
In this paper, the fractional variational iteration method (FVIM) was implemented to solve timefractional generalized Hirota-Satsuma coupled-KDV equation with modified Riemann-Liouville derivative. A new application of fractional variational iteration method (FVIM) was extended to derive analytical solutions in the form of a series for these equations. It is indicated that the solutions obtained by the FVIM are reliable and effective method for strongly nonlinear couple partial equations with modified Riemann-Liouville derivative. The effects of different fractional derivative for the coupled system are investigated.
- Derleme MakaleYalnız künye2014On the solutions of nonlinear fractional Klein-Gordon equation with modified Riemann-Liouville derivative
Merdan, Mehmet
In this paper, fractional variational iteration method (FVIM) is applied for finding approximate analytical solutions of nonlinear fractional Klein-Gordon equation. Time-fractional derivative is described in the Riemann-Liouville sense. A new application of fractional variational iteration method (FVIM) is extended to derive analytical solutions in the form of a series for this equation. The behavior of the solutions and the effects of different values of fractional order α are indicated graphically. It is shown that the solutions obtained by the FVIM are reliable, convenient and effective for strongly nonlinear partial equations with modified Riemann-Liouville derivative.
- MakaleAçık Erişim2013Numerical solution of the fractional-order Vallis systems using multi-step differential transformation method
Merdan, Mehmet
In this paper, we examine a fractional order Vallis systems. We also fulfil a detailed analysis on the stability of equilibrium. Multi-step differential transform method (MsDTM) extends to give approximate and analytical solutions of a fractional order Vallis systems. Numerical simulations are submitted to verify the validity and reliability results obtained from these methods.
- MakaleYalnız künye2013Adaptive multi-step differential transformation method to solve ODE systems
Gökdoǧan, Ahmet; Merdan, Mehmet
In this paper, it is given a fast algorithm to solve chaotic differential systems using the multi-step differential transforms method (MsDTM). The approach is applied to a number of chaotic nonlinear differential equations and numerical results are given. Performance analyses reveal that the proposed approach is an efficiency tool to solve using fewer time step to the considered equation systems.
- MakaleAçık Erişim2013On numerical solution to fractional non-linear oscillatory equations
Merdan, Mehmet; Gökdoǧan, Ahmet; Yildirim, Ahmet
In this article, the multi-step differential transform method (MsDTM) is applied to give approximate solutions of nonlinear ordinary differential equation such as fractional-non-linear oscillatory and vibration equations. The results indicate that the method is very effective and sufficient for solving non-linear differential equations of fractional order.
- MakaleAçık Erişim2013A numeric-analytic method for time-fractional Swift-Hohenberg (S-H) equation with modified Riemann-Liouville derivative
Merdan, Mehmet
In this paper, the fractional variational iteration method (FVIM) was applied to obtain the approximate solutions of time-fractional Swift-Hohenberg (S-H) equation with modified Riemann-Liouville derivative. A new application of fractional variational iteration method (FVIM) was extended to derive analytical solutions in the form of a series for these equations. Numerical results showed the FVIM is powerful, reliable and effective method when applied strongly nonlinear equations with modified Riemann-Liouville derivative.
- MakaleYalnız künye2013A multistage variational iteration method for solution of delay differential equations
Gökdoǧan, Ahmet; Merdan, Mehmet; Ertürk, Vedat Suat
In this paper, the approximate solution of delay differential equations is obtained by a reliable algorithm based on an adaptation of the classical variational iteration method (VIM), which is called the multi-stage variational iteration method (MSVIM). Examples are carried out and numerical results with comparison to exact solutions, VIM and MATLAB dde23 solver are given. The comparison reveals that the MSVIM is a promising tool to solve delay differential equations.
- MakaleYalnız künye2013Solution of time-fractional generalized Hirota-Satsuma coupled KdV equation by generalised differential transformation method
Merdan, Mehmet; Gökdogan, Ahmet; Yildirim, Ahmet; Mohyud-Din, Syed Tauseef
Purpose - In this article, the aim is to obtain an approximate analytical solution of time-fraction generalized Hirota-Satsuma coupled KDV with the help of the two dimensional differential transformation method (DTM). Exact solutions can also be obtained from the known forms of the series solutions. Design/methodology/approach - Two dimensional differential transformation method (DTM) is used. Findings - In this paper, the fractional differential transformation method is implemented to the solution of time-fraction generalized generalized Hirota-Satsuma coupled KDV with a number of initial and boundary values has been proved. DTM can be applied to many complicated linear and strongly nonlinear partial differential equations and does not require linearization, discretization, restrictive assumptions or perturbation. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial. Originality/value - This is an original work in which the results indicate that the method is powerful and significant for solving time-fraction generalized generalized Hirota-Satsuma coupled KDV type differential equations.
- MakaleYalnız künye2012The modified algorithm for the differential transform method to solution of Genesio systems
Gökdoĝan, Ahmet; Merdan, Mehmet; Yildirim, Ahmet
In this article, approximate analytical solution of chaotic Genesio system is acquired by the modified differential transform method (MDTM). The differential transform method (DTM) is mentioned in summary. MDTM can be obtained from DTM applied to Laplace, inverse Laplace transform and Padé approximant. The MDTM is used to increase the accuracy and accelerate the convergence rate of truncated series solution getting by the DTM. Results are given with tables and figures.
- MakaleYalnız künye2012Chaotic systems via multi-step differential transformation method
Yildirim, Ahmet; Gökdoǧan, Ahmet; Merdan, Mehmet
In this article, the multi-step differential transform method is implemented to give approximate and analytical solutions of nonlinear fractional order ordinary differential equation systems, such as Chen, Lorenz, Arneodo-Coullet, Genesio, Lui, and Rikitake chaotic systems. The numerical solutions obtained from the proposed method indicate that the approach is easy, simple, and accurate when applied to systems of fractional differential equations. Numerical simulations are given to verify the reliability and effectiveness of this method.
- MakaleYalnız künye2012Coupling of homotopy perturbation, Laplace transform and Padé approximants for nonlinear oscillatory systems
Merdan, Mehmet; Yildirim, Ahmet; Gökdogan, Ahmet; Mohyud-Din, Syed Tauseef
In this article, homotopy perturbation method coupled with Laplace transform and Padé 0approximants is applied on the re-formulated nonlinear oscillatory systems. Numerical results and graphical represenations explicitly reveal the complete reliability and effeicincy of the suggested algorithm.