A numerical method to solve the fractional diffusion equation, which could also be easily extended to many other fractional dynamics equations, is considered. These fractional equations have been proposed in order to describe anomalous transport characterized by non-Markovian kinetics and the breakdown of Fick’s law. In this paper we combine the forward time centered space (FTCS) method, well k...

A numerical method to solve the fractional diffusion equation, which could also be easily extended to many other fractional dynamics equations, is considered. These fractional equations have been proposed in order to describe anomalous transport characterized by non-Markovian kinetics and the breakdown of Fick’s law. In this paper we combine the forward time centered space (FTCS) method, well k...

We develop partial differential equation (PDE) methods to study the dynamics of pattern formation in partial integro-differential equations (PIDEs) defined on a spatially extended domain. Our primary focus is on scalar equations in two spatial dimensions. These models arise in a variety of neuronal modeling problems and also occur in material science. We first derive a PDE which is equivalent t...

It is known that the Laplace transform is frequently used to solve fractional-order differential equations. Unlike integer-order differential equations, fractional-order differential equations always lead to difficulties in calculating inversion of Laplace transforms. Motivated by finding an easy way to numerically solve the fractional-order differential equations, we investigated the validity ...

This paper deals with the application of fourth kind Chebyshev wavelets (FKCW) in solving numerically a model of HIV infection of CD4+T cells involving Caputo fractional derivative. The present problem is a system of nonlinear fractional differential equations. The goal is to approximate the solution in the form of FKCW truncated series. To do this, an operational matrix of fractional integrati...

The spine of an object is an entity that can characterise the object’s topology and describes the object by a lower dimension. It has an intuitive appeal for supporting geometric modelling operations. The aim of this paper is to show how a spine for a PDE surface can be generated. For the purpose of the work presented here an analytic solution form for the chosen PDE is utilised. It is shown th...

Chaos synchronization of coupled fractional order differential equation is receiving increasing attention because of its potential applications in secure communications and control processing. The aim of this paper is synchronization between two identical or different delay fractional-order chaotic systems in finite time. At first, the predictor-corrector method is used to obtain the solutions ...

Gaussian curvature is an important geometric property of surfaces, which has been used broadly in mathematical modeling. Due to the full nonlinearity curvature, efficient numerical methods for models based on it are uncommon literature. In this article, we propose operator-splitting method a general model. our method, decouple from differential operators by introducing two matrix- and vector-va...

This paper is devoted to the numerical computation of algebraic linear systems involving several matrix power functions; that finding x solution $$\sum _{\alpha \in \mathbb {R}}A^{\alpha }x=b$$ . These will be referred as Generalized Fractional Algebraic Linear Systems (GFALS). In this paper, we derive gradient methods for solving these very computationally complex problems, which themselves re...

Arithmetic Asian options are difficult to price and hedge, since at present, there is no closed-form analytical solution to price them. Transforming the PDE of the arithmetic the Asian option to a heat equation with constant coefficients is found to be difficult or impossible. Also, the numerical solution of the arithmetic Asian option PDE is not very accurate since the Asian option has low vol...