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.
- 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.