Two description forms of a linear fractional-order discrete system are considered. The first one is by a fractional-order difference equation, whereas the second by a fractional-order state-space equation. In relation to the two above-mentioned description forms, stability domains are evaluated. Several simulations of stable, marginally stable and unstable unit step responses of fractional-orde...

The numerical solution of a variable-order fractional financial system is calculated by using the Adams-Bashforth-Moulton method. The derivative is defined in the Caputo variable-order fractional sense. Numerical examples show that the Adams-Bashforth-Moulton method can be applied to solve such variable-order fractional differential equations simply and effectively. The convergent order of the ...

We develop a fast indirect collocation method for two-sided variable-order space-fractional diffusion equation, which models, e.g., the superdiffusive transport of solute in heterogeneous porous medium. Due to impact variable fractional order, stiffness matrix loses Toeplitz structure that is common context constant-order sFDEs. Consequently, discrete Fourier transform technique or convolution ...

Article history: Received 2 April 2014 Received in revised form 24 November 2014 Accepted 26 December 2014 Available online 5 January 2015

Based on high order approximation of L-stable RungeKutta methods for the Riemann-Liouville fractional derivatives, several classes of high order fractional Runge-Kutta methods for solving nonlinear fractional differential equation are constructed. Consistency, convergence and stability analysis of the numerical methods are given. Numerical experiments show that the proposed methods are efficien...