which satisfy both the fractional equation
(11) and boundary condition (13).
This fractional equation
is solved numerically by making use of the Adams-Bashforth-Moulton type method also known as predictor-corrector (PECE) technique and is fully detailed in the article by Diethelm et al.
For 1 < [alpha] < 2, the fractional equation
(1) is known as the fractional diffusion-wave equation which fills the gaps between the diffusion equation and wave equation [16,20].
Stojanovic: Existenceuniqueness result for a nonlinear n-term fractional equation
Clinical Calculations remains the only text to cover all four major drug calculation methods: basic formula, ratio and proportion, fractional equation
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Given the above discussions, in this paper, based on comparison principle of linear fractional equation
with delay, by applying a fractional inequality, a sufficient condition is achieved to ensure the synchronization of fractional order time delayed chaotic financial systems.
 used the difference method for space-time fractional equation
and presented the stability and convergence, Meerschaert and Tadjeran  applied the finite difference approximation for space-fractional equations, Meng  put forward a new approach for solving fractional partial differential equations, Sousa  developed numerical approximations for fractional diffusion equations via splines, Zhou and Wu  proposed the finite element multigrid method for the boundary value problem of fractional advection dispersion equation.
The task distribution model of the parallel algorithm  for the one-dimensional Riesz space fractional equation
For the case of [alpha] = 1, the fractional equation
reduces the classical Riccati differential equation.
The aim of this work is to contribute to the development of a new version of fractional fundamental Cattaneo-Vernotte equation applying the idea proposed in the work ; the order considered is (0,2] for the fractional equation
in spacetime domain; this representation preserves the dimensionality of the equation for any value taken by the exponent of the fractional derivative.
In order to illustrate two analytical methods, we investigate the nonlinear local fractional equation
of order 2[alpha] as follows:
Considering (11) and assuming that the space derivative is fractional (9) and the time derivative is ordinary, the spatial fractional equation