Modeling with fractional difference equations

On Some Fractional Systems of Difference Equations

This paper deal with the solutions of the systems of difference equations $$x_{n+1}=frac{y_{n-3}y_nx_{n-2}}{y_{n-3}x_{n-2}pm y_{n-3}y_n pm y_nx_{n-2}}, ,y_{n+1}=frac{y_{n-2}x_{n-1}}{ 2y_{n-2}pm x_{n-1}},,nin mathbb{N}_{0},$$ where $mathbb{N}_{0}=mathbb{N}cup left{0right}$, and initial values $x_{-2},, x_{-1},,x_{0},,y_{-3},,y_{-2},,y_{-1},,y_{0}$ are non-zero real numbers.

Oscillation of Fractional Nonlinear Difference Equations

The oscillation criteria for forced nonlinear fractional difference equation of the form ∆x(t) + f1(t, x(t+ α)) =v(t) + f2(t, x(t+ α)), t ∈ N0, 0 < α ≤ 1, ∆x(t)|t=0 =x0, where ∆α denotes the Riemann-Liouville like discrete fractional difference operator of order α is presented. Mathematics Subject Classification: 26A33, 39A12

Finite difference Methods for fractional differential equations

In this review paper, the finite difference methods (FDMs) for the fractional differential equations are displayed. The considered equations mainly include the fractional kinetic equations of diffusion or dispersion with time, space and time-space derivatives. In some way, these numerical methods have similar form as the case for classical equations, some of which can be seen as the generalizat...

Fractional differential equations with Legendre polynomials

Two-dimensional Fractional System of Nonlinear Difference Equations in the Modeling Competitive Populations

In this paper we have already investigated the solutions of the two-dimensional fractional system of nonlinear difference equations in the modeling competitive populations in the form 1 1 1 1 1 1 & n n n n n n n n x y x y x y y x             (1) where  and  are real numbers with the initial conditions 1 0 1 , , , x x y   and 0 y such that 1 0 x y    and 1 0 y x    . Moreov...