Showing papers by "Mehmet Merdan published in 2016"

Mathematical Modeling of Dengue Disease under Random Effects

Abstract: In this study, the deterministic mathematical model of Dengue disease is examined under Laplacian random effects. Random variables with Laplace distribution are used for randomizing the deterministic parameters. Simulations of the numerical results of the equation system are made with Monte-Carlo methods and the results are used for commenting on the disease. Comments are made on the random behavior of the components of the model after the calculation of their numerical characteristics like the expected value, variance, standard deviation, confidence interval and moments along with the coefficients of skewness and kurtosis from the results of the simulations. Results from the deterministic model are compared with the results from the random model to point out the possible contribution of random modeling to mathematical analysis studies on the disease.

Mathematical Modeling of Biochemical Reactions Under Random Effects

Abstract: In this study, random effects are added to the parameters of the deterministic Biochemical Reaction Model (BRM) to form a system of random differential equations. A random model is built with these equations to describe the random behavior of biochemical reactions. Gaussian and Beta distributions are used for the random effect terms. Numerical characteristics of the random model are investigated using the simulations of the random equation system. Characteristics of the model components under Gaussian and Beta distributed effects are compared and comments are made on the difference in these two cases. The results are also used to explore the differences in the deterministic and random models of BRM and to study the random behavior of the model components.

On the fractional riccati differential equation

Abstract: In this paper, We tried to find an analytical solution of nonlinear Riccati con- formable fractional differential equation. Fractional derivatives are described in the con- formable derivative. The behavior of the solutions and the effects of different values of frac- tional orderare 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).

Analytical Approximate Solutions of Fractional Convection-Diffusion Equation by Means of Local Fractional Derivative Operators

Abstract: In this article, the local fractional decomposition method ( LFDM) is applied to obtain approximate the analytical solution of nonlinear fractional convection-dif fusion. Numerical solutions obtained by local fractional decomposition method are compared with the exact solutions, revealing that the obtained solutions are of high accuracy. A new application of loca l fractional decomposition method (LFDM) was extended to reproduce the analytical solutions to this equati on in the form of a series. It is shown that the solutions obtained by the LFDM are reliable, simple and t hat LFDM is an effective method for strongly nonlinear partial equations.

On The Solutions of Nonlinear Fractional Klein-Gordon Equation by Means of Local Fractional Derivative Operators

Abstract: In this paper, an application of the local fractional decomposition method (LFDM) is analyzed to search for an approximate analytical solution of nonlinear fractional Klein-Gordon equation. The fractional derivatives are described in Jumarie’s modified Riemann-Liouville sense. A new application of the local fractional decomposition method (LFDM) is extended to derive the approximate solutions in series form for this model problem. Solutions have been plotted for di erent values of the fractional order. It is concluded that the solutions for nonlinear partial equations with Riemann- Liouville derivative obtained with LFDM are useful, reliable and efficient.