Based on the recently introduced fractional Taylor’s formula, a fractional heat conduction constitutive equation is formulated by expanding the single-phase lag model using the fractional Taylor’s formula. Combining with the energy balance equation, the derived fractional heat conduction equation has been shown to be capable of modeling diffusion-to-Thermal wave behavior of heat propagation by ...

in this paper, we prove the existence of the solution for boundary value prob-lem(bvp) of fractional dierential equations of order q 2 (2; 3]. the kras-noselskii's xed point theorem is applied to establish the results. in addition,we give an detailed example to demonstrate the main result.

In this paper, the fractional partial differential equations are defined by modified Riemann-Liouville fractional derivative. With the help of fractional derivative and fractional complex transform, these equations can be converted into the nonlinear ordinary differential equations. By using solitay wave ansatz method, we find exact analytical solutions of the space-time fractional Zakharov Kuz...

This paper address a new vision for the generalized Mittag-Leffler stability of the fractional differential equations. We mainly focus on a new method, consisting of decomposing a given fractional differential equation into a cascade of many sub-fractional differential equations. And we propose a procedure for analyzing the generalized Mittag-Leffler stability for the given fractional different...

in this paper, operational matrices of riemann-liouville fractional integration and caputo fractional differentiation for shifted jacobi polynomials are considered. using the given initial conditions, we transform the fractional differential equation (fde) into a modified fractional differential equation with zero initial conditions. next, all the existing functions in modified differential equ...

In this paper we present a numerical method for fuzzy differential equation of fractional order under gH-fractional Caputo differentiability. The main idea of this method is to approximate the solution of fuzzy fractional differential equation (FFDE) by an implicit method as corrector and explicit method as predictor. This method is tested on numerical examples.

In this paper, operational matrices of Riemann-Liouville fractional integration and Caputo fractional differentiation for shifted Jacobi polynomials are considered. Using the given initial conditions, we transform the fractional differential equation (FDE) into a modified fractional differential equation with zero initial conditions. Next, all the existing functions in modified differential equ...

in this paper, a new fractional sub-equation method is proposed for finding exact solutions of fractional partial differential equations (fpdes) in the sense of modified riemann-liouville derivative. with the aid of symbolic computation, we choose the space-time fractional zakharov-kuznetsov-benjamin-bona-mahony (zkbbm) equation in mathematical physics with a source to illustrate the validity a...

We study the asymptotic behavior of the rst eigenvalue and eigenfunction of a one-dimensional periodic elliptic operator with Neumann boundary conditions. The second order elliptic equation is not self-adjoint and is singularly perturbed since, denoting by ε the period, each derivative is scaled by an ε factor. The main di culty is that the domain size is not an integer multiple of the period. ...

in this paper, a numerical efficient method is proposed for the solution of time fractionalmobile/immobile equation. the fractional derivative of equation is described in the caputosense. the proposed method is based on a finite difference scheme in time and legendrespectral method in space. in this approach the time fractional derivative of mentioned equationis approximated by a scheme of order o...