The proposed research paper shall analyze a method of image change detection based upon the Fractional Fourier transform (FrFT), which can provide results with good precision and better recall values obtained by optimizing its fractional order 'a'. The method is analyzed because, with extra degree of freedom provided by the Discrete Fractional Fourier Transform (DFrFT), we can get mor...

We consider a fractional-order model of two asymmetrically coupled spiking neurons. The dynamical behavior of the two neurons is modeled by the fractional-order Hodgkin-Huxley equations. Simulations of the model for distinct values of the order of the fractional derivative, α, and of the coupling constants, k1, k2, show interesting features, such as relaxation oscillations, mixed-mode oscillati...

Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the same idea for fractional variational problems. We consider a minimization problem with a Lagrangian that depends on the left Riemann– Liouville fractional deri...

In this paper, a novel image denoising algorithm named fractional integral image denoising algorithm (FIIDA) is proposed, which based on fractional calculus Riemann-Liouville definition. The structures of n*n fractional integral masks of this algorithm on the directions of 135 degrees, 90 degrees, 45 degrees, 0 degrees, 180 degrees, 315 degrees, 270 degrees and 225 degrees are constructed and d...

A fiber-tracking algorithm was used to extract fractional anisotropy of bilateral cingulum bundles in patients with probable Alzheimer's disease and normal aging controls. In addition, their hippocampal volumes were measured manually. Relative to normal controls, Alzheimer's disease patients showed a significant reduction of fractional anisotropy and hippocampal volumes. Significant correlation...

‎It is commonly accepted that fractional differential equations play‎ ‎an important role in the explanation of many physical phenomena‎. ‎For‎ ‎this reason we need a reliable and efficient technique for the‎ ‎solution of fractional differential equations‎. ‎This paper deals with‎ ‎the numerical solution of a class of fractional differential‎ ‎equation‎. ‎The fractional derivatives are described...

In this paper, a novel digital image denoising algorithm called generalized fractional integral filter is introduced based on the generalized Srivastava-Owa fractional integral operator. The structures of n×n fractional masks of this algorithm are constructed. The denoising performance is measured by employing experiments according to visual perception and PSNR values. The results demonstrate t...

in this article we implement an operational matrix of fractional integration for legendre polynomials. we proposed an algorithm to obtain an approximation solution for fractional differential equations, described in riemann-liouville sense, based on shifted legendre polynomials. this method was applied to solve linear multi-order fractional differential equation with initial conditions, and the...

From numerical simulation and analytical modeling it is shown that fast ions can resonate with plasma waves at fractional values of the particle drift-orbit transit frequency when the plasma wave amplitude is sufficiently large. The fractional resonances, which are caused by a nonlinear interaction between the particle orbit and the wave, give rise to an increased density of resonances in phase...

The problem of fractional heat conduction in a composite medium consisting of a spherical inclusion ) 0 ( R r   and a matrix ) (    r R being in perfect thermal contact at R r  is considered. The heat conduction in each region is described by the time-fractional heat conduction equation with the Caputo derivative of fractional order 2 0   and , 2 0    respectively. The Laplace trans...