The paper deals with fractional derivative introduced by means of Fourier transform. The explicit form of the kernel of general derivative operator acting on the functions analytic on a curve in complex plane is deduced and the correspondence with some well known approaches is shown. In particular it is shown how the uniqueness of the operation depends on the derivative order type (integer, rat...

in this paper, the sinc collocation method is proposed for solving linear and nonlinear multi-order fractional differential equations based on the new definition of fractional derivative which is recently presented by khalil, r., al horani, m., yousef, a. and sababeh, m. in a new definition of fractional derivative, j. comput. appl. math. 264 (2014), 65{70. the properties of sinc functions are ...

In this article, the local fractional Homotopy perturbation method is utilized to solve the non-homogeneous heat conduction equations. The operator is considered in the sense of the local fractional differential operator. Comparative results between non-homogeneous and homogeneous heat conduction equations are presented. The obtained result shows the non-differentiable behavior of heat conducti...

By space-fractional (or L evy-Feller) diiusion processes we mean the processes governed by a generalized diiusion equation which generates all L evy stable probability distributions with index (0 < 2), including the two symmetric most popular laws, Cauchy (= 1) and Gauss (= 2). This generalized equation is obtained from the standard linear diiusion equation by replacing the second-order space d...

In this paper, based on the developed nonlinear fourth-order operator and method of order reduction, a novel compact difference scheme is constructed for mixed-type time-fractional Burgers’ equation, from which L1-discretization formula applied to deal with terms fractional derivative, convection term discretized by operator. Then fully discrete L1 uniform meshes can be established approximatin...

In this article, the local fractional variational iteration method is proposed to solve nonlinear partial differential equations within local fractional derivative operators. To illustrate the ability and reliability of the method, some examples are illustrated. A comparison between local fractional variational iteration method with the other numerical methods is given, revealing that the propo...

In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...

Recently, a new fractional derivative operator has been introduced so that it presents the combination of Riemann–Liouville integral and Caputo derivative. This paper aims to enhance reproducing kernel Hilbert space method (RKHSM, for short) solving certain differential equations involving this is first time application RKHSM employed some with operator. We illustrate convergence analysis appli...