Fractional Differential Equations

高等学校計算数学学報 = Numerical mathematics

Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks

Advanced Local Fractional Calculus and Its Applications

http://ieeexplore.ieee.org/iel5/5/31196/01451889.pdf

Random differential equations in science and engineering

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.

/pdf/mathematical-modeling-of-dengue-disease-under-random-effects-1xfaak3jeo.pdf

Mathematical Modeling of Dengue Disease under Random Effects

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.

Mathematical Modeling of Biochemical Reactions Under Random Effects

This paper investigates the accuracy of the differential transformation method (DTM) for solving the three-species food chain models which is described as three-dimensional system of ODES with quadratic and rational nonlinearities. Numerical results are compared to those obtained by the fourth-order Runge-Kutta method to illustrate the preciseness and effectiveness of the proposed method. The direct symbolic-numeric scheme is indicated to be efficient and accurate.

	 

	Key words: Three-species food chain models, multi-step differential transformation method, attractors.

A numeric-analytic method for approximating three-species food chain models

Abstract 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.

A Multistage Variational Iteration Method for Solution of Delay Differential Equations

In this article, local fractional decomposition method (LFDM) is applied to obtain an analytical approximate solution of nonlinear time-fractional Gas dynamics equation. A new application of local fractional decomposition method (LFDM) was extended to derive analytical solutions in the form of a convergent series with easily computable components, requiring no linearization or small perturbation for this equation. The solutions obtained by LFDM have been shown to be reliable, simple and the method is an effective technique for strong nonlinear partial equations. AMS Subject Classification: 35R11, 26A33

/pdf/local-fractional-derivative-operators-method-for-solving-5f7fo2wq7h.pdf

Mehmet Merdan

Papers

Mathematical Modeling of Dengue Disease under Random Effects

Mathematical Modeling of Biochemical Reactions Under Random Effects

A numeric-analytic method for approximating three-species food chain models

A Multistage Variational Iteration Method for Solution of Delay Differential Equations

Local fractional derivative operators method for solving nonlinear gas dynamic equation of fractional order