n this paper, at first the  concept of Caputo fractionalderivative is generalized on time scales. Then the fractional orderdifferential equations are introduced on time scales. Finally,sufficient and necessary conditions are presented for the existenceand uniqueness of solution of initial valueproblem including fractional order differential equations.

In this paper, we introduced a novel variational iteration method (VIM) for solving fractional wave–like and heat–like equations in a large domain which is improved by adding an auxiliary parameter. The suggested method is very effective and we can control the convergence region very easily. By solving some fractional wave-like and heat-like equations with the proposed method and comparing with...

The aim of this work is to describe the qualitative behavior of the solution set of a given system of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. In order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. This is done by the extension of...

the complex-step derivative approximation is applied to compute numerical derivatives. in this study, we propose a new formula of fractional complex-step method utilizing jumarie definition. based on this method, we illustrated an approximate analytic solution for the fractional cauchy-euler equations. application in image denoising is imposed by introducing a new fractional mask depending on s...

Distributed-order time-fractional wave equations appear in the modeling of propagation viscoelastic media. The material characteristics medium are modeled through constitutive functions or distributions distributed-order law. In this work we propose to take positive Radon measures for "functions". First, derive a thermodynamical restriction on which is easy check, and therefore suitable applica...