Abstract: The paper presents the simulation toolkit in MATLAB/Simulink R © for the fractional order discrete, state-space system education. The toolkit has been written as a set of C-MEX S-functions which simulate several fractional order blocks e.g. fractional order difference, fractional order discrete state-space representation, fractional order Kalman filter. This way the C code generation ...

We consider a fractional version of the classical non-linear birth process of which the YuleFurry model is a particular case. Fractionality is obtained by replacing the first-order time derivative in the difference-differential equations which govern the probability law of the process, with the Dzherbashyan-Caputo fractional derivative. We derive the probability distribution of the number Nν (t...

Fractional diffusion equations are abstract partial differential equations that involve fractional derivatives in space and time. They are useful to model anomalous diffusion, where a plume of particles spreads in a different manner than the classical diffusion equation predicts. An initial value problem involving a space-fractional diffusion equation is an abstract Cauchy problem, whose analyt...

OBJECTIVE To explore the diagnostic usefulness of high b-value diffusion magnetic resonance brain imaging ("q-space" imaging) in multiple sclerosis (MS). More specifically, we aimed at evaluating the ability of this methodology to identify tissue damage in the so-called normal-appearing white matter (NAWM). DESIGN In this study we examined the correlation between q-space diffusion imaging and...

Dropping probability of handoff calls and blocking probability of new calls are two important QoS measures for cellular networks. Since the dropping probability of handoff calls is more important, call admission policies are used to maintain the upper bound of dropping probability of handoff calls. The fractional guard channel policy (FG) is a general call admission policy and includes most pri...

In this article, the modified simple equation method has been extended to celebrate the exact solutions of nonlinear partial time-space differential equations of fractional order. Firstly, the fractional complex transformation has been implemented to convert nonlinear partial fractional differential equations into nonlinear ordinary differential equations. Afterwards, modified simple equation m...

This paper deals with the investigation of the computational solutions of a unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the generalized Riemann–Liouville fractional derivative defined by others and the space derivative of second order by the Riesz–Feller fractional derivative and adding...