The aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (PDE) in the electroanalytical chemistry. The space fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the Grunwald- Letnikov discretization of the Ri...

the aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (pde) in the electroanalytical chemistry. the space fractional derivative is described in the riemann-liouville sense. in the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the grunwald- letnikov discretization of the ri...

The previous work in [1], Tseng et al. have designed a fractional order differentiator using radial basis function by directly truncating the coefficients to approximate the fractional order derivative Dα of the given digital signal. This paper presents the designing of fractional order differentiator using radial basis function and window. Three design examples are given to illustrate that the...

Stochastic differential equations (SDEs) have been applied by engineers and economists because it can express the behavior of stochastic processes in compact expressions. In this paper, by using Grunwald-Letnikov fractional derivative, the stochastic differential model is improved. Two numerical examples are presented to show efficiency of the proposed model. A numerical optimization approach b...

The theory of derivative of noninteger order goes back to Leibniz, Liouville, Riemann, Grunwald and Letnikov. Derivatives of fractional order have found many applications in recent studies in mechanics, physics, economics, medicine.Classes of fractional differentiable systems have studied in [10], [4]. In the first section the fractional tangent bundle to a differentiable manifold is defined, u...

Space fractional derivatives have been used instead of integer operators with success in a variety of practical applications to study and describe transport processes in media characterized by spatial connectivity properties and high structural heterogeneity altering the classical laws of diffusion. This study provides an implementation of space fractional FitzHugh-Nagumo model of excitable med...

In this article, the fractional-order differential equation of particle sedimentation was obtained. It considers Basset force’s fractional origin and contains Riemann–Liouville integral rewritten as a Grunwald–Letnikov derivative. As result, general solution proposed found analytically. The belonging to real range values strictly theoretically proven. obtained validated on particular analytical...

At present, fractional differential is the effective mathematical approach which deals with factual problems. This projected technique employs derivatives definitions Riemann-Liouville (R-L), Grunwald-Letnikov (G-L) and caputo for denoising medical image. The presented method based on derivative in turn improves quality of input image processed integer order such as pre-processing operation, co...

-This paper deals with hybrid projective synchronization between a fractional order Volta chaotic system and Genesio Tesi chaotic system by using tracking control and stability theory of fractional order system. An effective controller is designed to synchronize these two systems. Numerical simulations have been done by using MATLAB. Numerical solutions via Grunwald-Letnikov method has been use...

Underwater images usually suffer from degraded visibility. Light attenuates and scatters in water resulting in low contrast and haziness in the scenes. Therefore, the main problems to be dealt with in underwater environment are poor contrast, non-uniform lighting, haziness and blurring. Hence, in order to study underwater images, it becomes utmost important to extract the invisible or unclear e...