In this paper, a space fractional diffusion equation (SFDE) with nonhomogeneous boundary conditions on a bounded domain is considered. A new matrix transfer technique (MTT) for solving the SFDE is proposed. The method is based on a matrix representation of the fractional-in-space operator and the novelty of this approach is that a standard discretisation of the operator leads to a system of lin...

This paper studies the distribution of avalanches in fractional cascading, linking the behavior to studies on self-organized criticality, in particular, the power law behavior of the Bak-Tang-Wiesenfeld sandpile model. Unlike the sandpile model, however, we prove that fractional cascading does not exhibit abelian properties. While fractional cascading has maximum gap size as a system parameter ...

In this present work, the fractional derivatives in the sense of modified Riemann-Liouville derivative and the direct algebraic method are employed for constructing the exact complex solutions of non-linear time-fractional partial differential equations. The power of this manageable method is presented by applying it to several examples. Reference to this paper should be made as follows: Taghiz...

This paper analyzes reduction of fractional ideals in a purely cubic function field of unit rank one. The algorithm is used for generating all the reduced principal fractional ideals in the field, thereby finding the fundamental unit or the regulator, as well as computing a reduced fractional ideal equivalent to a given nonreduced one. It is known how many reduction steps are required to achiev...

In this paper, using the Lie group analysis method, we study the invariance properties of the general time fractional fifth-order Korteweg-de Vries (KdV) equation. A systematic research to derive Lie point symmetries of the equation is performed. In the sense of point symmetry, all of the geometric vector fields and the symmetry reductions of the equation are obtained, the exact power series so...

The modified fractional integral operators, introduced in [4], are proved to be bounded from some Lp– space into some Lq– space with power-logarithmic weights.

Diffusion magnetic resonance imaging (dMRI) is an emerging medical technique used for describing water diffusion in an organic tissue. Typically, rank-2 tensors quantify this diffusion. From this quantification, it is possible to calculate relevant scalar measures (i.e. fractional anisotropy and mean diffusivity) employed in clinical diagnosis of neurological diseases. Nonetheless, 2nd-order te...

Consumer products like foods contain numerous polymeric and particulate additives that play critical roles in maintaining their stability, quality and function. The resulting materials exhibit complex bulk and interfacial rheological responses, and often display a distinctive power-law response under standard rheometric deformations. These power-laws are not conveniently described using convent...

This paper presents a new strategy to simulate fractional frequency synthesizer behavioral models with better performance and reduced simulation time. The models are described in Verilog-A with accurate phase noise predictions and they are based on a time jitter to power spectral density transformation of the principal noise sources in a synthesizer. The results of a fractional frequency synthe...

We present two observations related to the application of linear (LFE) and nonlinear fractional equations (NFE). First, we give the comparison and estimates of the role of the fractional derivative term to the normal diffusion term in a LFE. The transition of the solution from normal to anomalous transport is demonstrated and the dominant role of the power tails in the long time asymptotics is ...