Sürdürülebilir Kalkınma Amaçları
Yayınlar
- Kitap BölümüYalnız künye2025Scopus SJRQ4Investigation of Fractional Order Genesio-Tesi System Using Laplace Transformation
Bekiryazici, Zafer; Sengul, Suleyman; Merdan, Mehmet
In this paper the fractional-order Genesio-Tesi chaotic system is investigated with Laplace transformation method. Genesio-Tesi system is a three-dimensional equation system with quadratic nonlinearity and is frequently used for exemplifying chaotic systems. In this study, Caputo fractional derivative is used to obtain the fractional system and Laplace transformation is applied in order to analyze the explicit solutions of the system.
- MakaleAçık Erişim2024Scopus SJRQ2Approximate Solutions of Fractional Differential Equations Using Optimal q-Homotopy Analysis Method: A Case Study of Abel Differential Equations
Şengül, Süleyman; Bekiryazici, Zafer; Merdan, Mehmet
In this study, the optimal q-Homotopy Analysis Method (optimal q-HAM) has been used to investigate fractional Abel differential equations. This article is designed as a case study, where several forms of Abel equations, containing Bernoulli and Riccati equations, are given with ordinary derivatives and fractional derivatives in the Caputo sense to present the application of the method. The optimal q-HAM is an improved version of the Homotopy Analysis Method (HAM) and its modification q-HAM and focuses on finding the optimal value of the convergence parameters for a better approximation. Numerical applications are given where optimal values of the convergence control parameters are found. Additionally, the correspondence of the approximate solutions obtained for these optimal values and the exact or numerical solutions are shown with figures and tables. The results show that the optimal q-HAM improves the convergence of the approximate solutions obtained with the q-HAM. Approximate solutions obtained with the fractional Differential Transform Method, q-HAM and predictor–corrector method are also used to highlight the superiority of the optimal q-HAM. Analysis of the results from various methods points out that optimal q-HAM is a strong tool for the analysis of the approximate analytical solution in Abel-type differential equations. This approach can be used to analyze other fractional differential equations arising in mathematical investigations.
AtıfScopus4WoS5OpenAlex5
İncele - MakaleAçık Erişim2022Scopus SJRQ3A MODIFICATION OF APPROXIMATE RANDOM CHARACTERISTICS FOR A MODEL OF ZIKA VIRUS TRANSMISSION
Bekiryazici, Zafer; Kesemen, Tulay; Merdan, Mehmet; Khaniyev, Tahir
In this study, a theoretical model of Zika virus transmission is investigated with random parameters. The parameters of a deterministic model are transformed to random variables to obtain a system of random differential equations. The approximate solutions of the model are analyzed with modified random differential transformation method. It is seen that modified random differential transformation method performs better than random differential transformation method on long time intervals
AtıfOpenAlex1İncele - MakaleAçık Erişim2022Scopus SJRQ4Transmission of Cholera Disease with Laplacian and Triangular Parameters
Merdan, Mehmet; Bekiryazici, Zafer; Kesemen, Tulay; Khaniyev, Tahir
A mathematical model has been introduced for the transmission dynamics of cholera disease by GQ Sun et al. recently. In this study, we add Laplacian and Triangular random effects to this model and analyze the variation of results for both cases. The expectations and co-efficients of variation are compared for the random models and the results are used to comment on the differences and similarities between the effects of these probability distributions. The randomness of the model itself is also investigated through comparison of the random and deterministic outcomes.
AtıfOpenAlex1İncele - MakaleAçık Erişim2021Scopus SJRQ3Wong-Zakai Method for Stochastic Differential Equations in Engineering
Sengul, Suleyman; Bekiryazici, Zafer; Merdan, Mehmet
In this paper, Wong-Zakai approximation methods are presented for some stochastic differential equations in engineering sciences. Wong-Zakai approximate solutions of the equations are analyzed and the numerical results are compared with results from popular approximation schemes for stochastic differential equations such as Euler-Maruyama and Milstein methods. Several differential equations from engineering problems containing stochastic noise are investigated as numerical examples. Results show that Wong-Zakai method is a reliable tool for studying stochastic differential equations and can be used as an alternative for the known approximation techniques for stochastic models.
AtıfScopus4WoS4OpenAlex5İncele - MakaleYalnız künye2021Scopus SJRQ3Modification of the random differential transformation method and its applications to compartmental models
Bekiryazici, Zafer; Merdan, Mehmet; Kesemen, Tulay
In this study, a modification of the random differential transformation method is given by using Laplace-Padé method. The modification, which has previously been introduced for the deterministic differential transformation method (DTM), is used to obtain improved approximate expected values, variances, and confidence intervals for systems of random differential equations. Comparison of approximate results obtained from the random differential transformation method and the modified method are given to underline the improvement of the approximations. Epidemiological compartmental models of type SIR and SIIR are used to implement the modified method and demonstrate its advantages. Simulations and deterministic counterparts of the models are also investigated to confirm the suitability of the results of the approximations.
AtıfScopus14WoS12OpenAlex19İncele - MakaleAçık Erişim2018Scopus SJRQ3ANALYZING 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.
AtıfScopus3WoS2OpenAlex3İncele - 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.
AtıfScopus1WoS1İncele - MakaleAçık Erişim2017Scopus SJRQ1Deterministic 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.
AtıfScopus10WoS10OpenAlex13
İncele - MakaleAçık Erişim2017Scopus SJRQ2Comparison 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.
AtıfScopus25WoS25OpenAlex25İncele