Merdan, Mehmet; Bekiryazıcı, Zafer; Kesemen, Tülay

In this study, the classical epidemic model of Kermack and McKendrick is analyzed with beta distributed random components. A random analysis is done for the deterministic epidemic model by transforming the parameters and initial values of the system to random variables with beta distribution. The approximations for the expectations of the model variables are compared with the deterministic results to comment on the randomness of the cases with random parameters and random initial values. Results for some numerical characteristics of these two cases are also given to investigate the accuracy of the approximations for the expected values.

Anaç, Halil; Merdan, Mehmet; Kesemen, Tülay

In this study, the solution of a random component heat equation is obtained by using Crank-Nicolson Method. The initial condition of this equation is examined by Normal distribution. The expected value and variance of solution of this equation are obtained. Crank-Nicolson method is applied to analyze the solution of this equation. Also, the solution and the graphs of the expected value and variance are obtained by using MATLAB software. The results of the heat equation are compared with random characteristics of this equation. Firstly, a random component heat equation is solved by this method.

Anaç, Halil; Merdan, Mehmet; Kesemen, Tülay

The new Sumudu transform iterative method is implemented to get the approximate solutions of random component time-fractional partial differential equations with Caputo derivative. The parameters and the initial conditions of the random component time-fractional partial differential equations are analyzed with Gamma distribution. The expected values and variances of these solutions are calculated, and the graphs of the expected values and variances are plotted in Maple software. The results for the random component time-fractional partial differential equations with Gamma distribution are examined to investigate effects of this distribution on results. The numerical experiments indicate that this method is very effective.

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.

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.