Various scholars have lately employed a wide range of strategies to resolve specific types symmetrical fractional differential equations. This paper introduces new implicit finite difference method with variable-order time-fractional Caputo derivative solve semi-linear initial boundary value problems. Despite its extensive use in other areas, calculus has only recently been applied physics. aim...

The chaotic dynamics of fractional (non-integer) order systems have begun to attract much attention in recent years. In this paper, we study the projective synchronization in two coupled fractional order chaotic oscillators. It is shown that projective synchronization can also exist in coupled fractional order chaotic systems. A simple feedback control method for controlling the scaling factor ...

The theory of fractional calculus goes back to the beginning of the theory of di erential calculus but its inherent complexity postponed the application of the associated concepts. In the last decade the progress in the areas of chaos and fractals revealed subtle relationships with the fractional calculus leading to an increasing interest in the development of the new paradigm. In the area of a...

In this paper, by utilizing the fractional calculus theory and computer simulations, dynamics of the fractional order system is studied. Further, we have extended the nonlinear feedback control in ODE systems to fractional order systems, in order to eliminate the chaotic behavior. The results are proved analytically by stability condition for fractional order system. Moreover numerical simulati...

Nowadays, fractional calculus are used to model various different phenomena in nature, but due to the non-local property of the fractional derivative, it still remains a lot of improvements in the present numerical approaches. In this paper, some new numerical approaches based on piecewise interpolation for fractional calculus, and some new improved approaches based on the Simpson method for th...

<abstract><p>The aim of this work is to study several problems the calculus variations, where dynamics state function given by a generalized fractional derivative. This derivative combines two well-known concepts: with respect another and variable order. We present Euler–Lagrange equation, which necessary condition that every optimal solution problem must satisfy. Other are also stu...

In this paper, we introduce fractional calculus into image inpainting and propose a new class of fractional-order variational image inpainting models, in both space and wavelet domains, inspired by the works of Bai and Feng. The corresponding Euler-Lagrange equations are given and proper numerical algorithm is analyzed. According to the simulations on several testing images, our algorithm demon...

fractional calculus is the field of mathematical analysis which deals with the investigation and applications of integrals and derivatives of arbitrary order.the purpose of this work is to use hadamard fractional integral to establish some new integral inequalities of gruss type by using one or two parameters which ensues four main results . furthermore, other integral inequalities of reverse m...

The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which are used in the physics during the past few years, will be briefly described in this paper. We solve some problems of consistent formulations of FVC by using ...