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, three Ito stochastic differential equations with multiplicative noise are investigated with Wong-Zakai method. The stochastic differential equations are also analyzed by Euler-Maruyama, Milstein and Runge Kutta stochastic approximation methods. The relative errors of these three methods are compared and the performance of Wong-Zakai method is shown alongside numerical results.

/pdf/wong-zakai-method-applications-for-explicitly-solvable-xgbsdo6rf2.pdf

Wong-Zakai Method Applications for Explicitly Solvable Stochastic Differential Equations

Bu calismada Kermack ve McKendrick’in klasik salgin hastalik modeli beta dagilimina sahip rastgele bilesenlerle incelenmektedir. Deterministik model icin sistemin parametreleri ve baslangic kosullari beta dagilimina sahip rastgele degiskenlere donusturulerek bir rastgele inceleme yapilmaktadir. Model degiskenlerinin beklenen degerleri icin elde edilen yaklasimlar deterministik sonuclarla karsilastirilarak rastgele baslangic kosullari ve rastgele parametre iceren durumlarin rastgele yapilari hakkinda yorum yapilmaktadir. Beklenen degerlerin yaklasimlarinin dogrulugunun incelenmesi icin iki durumun bazi sayisal karakteristiklerinin sonuclari da verilmektedir.

/pdf/analysis-of-the-dynamics-of-the-classical-epidemic-model-1xzs9u07ik.pdf

Analysis of The Dynamics of The Classical Epidemic Model with Beta Distributed Random Components

Coullet sistemi olarak bilinen nonlineer denklem sisteminin cozumu diferensiyel donusum yontemi ile elde edildi. Sayisal sonuclar, onerilen yontemin etkinligini ve dogrulugunu gostermek icin dorduncu mertebeden Runge-Kutta yontemi ile karsilastirildi. Onerilen yontemin guclu, dogru ve kolayca uygulanabilirligi gosterildi.

/pdf/on-solving-coullet-system-by-differential-transformation-4lfg47zg0s.pdf

On Solving Coullet System by Differential Transformation Method

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.

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

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.

/pdf/the-new-sumudu-transform-iterative-method-for-studying-the-4lu3fz11u2.pdf

Mehmet Merdan

Papers

Wong-Zakai Method Applications for Explicitly Solvable Stochastic Differential Equations

Analysis of The Dynamics of The Classical Epidemic Model with Beta Distributed Random Components

On Solving Coullet System by Differential Transformation Method

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

The New Sumudu Transform Iterative Method For Studying The Random Component Time-Fractional Klein-Gordon Equation