Fractional neutron transport equation reflects the anomalous processes in nuclear reactor. In this paper, we will construct fully discrete methods for type of fractional with Riesz derivative, where generalized WENO5 scheme is used spatial direction and Runge–Kutta schemes are adopted temporal direction. The linear stabilities different stages order ERK discussed detailed. Numerical examples sh...

Abstract In this paper, the Riesz-Caputo fractional derivative of variable order with fixed memory is considered. The studied non-integer differential operator approximated by means modified basic rules numerical integration. three proposed methods are based on polynomial interpolation: piecewise constant, linear, and quadratic interpolation. errors generated described experimental rate converg...

A universal approach by Laplace transform to the variational iteration method for fractional derivatives with the nonsingular kernel is presented; in particular, the Caputo-Fabrizio fractional derivative and the Atangana-Baleanu fractional derivative with the non-singular kernel is considered. The analysis elaborated for both non-singular kernel derivatives is shown the necessity of considering...

Fractional differential equations have attracted considerable interest because of their ability to model anomalous transport phenomena. Space fractional diffusion equations with a nonlinear reaction term have been presented and used to model many problems of practical interest. In this paper, a two-dimensional Riesz space fractional diffusion equation with a nonlinear reaction term (2D-RSFDE-NR...

the purpose of this paper is to study the fuzzy fractional differentialequations. we prove that fuzzy fractional differential equation isequivalent to the fuzzy integral equation and then using this equivalenceexistence and uniqueness result is establish. fuzzy derivative is considerin the goetschel-voxman sense and fractional derivative is consider in theriemann liouville sense. at the end, we...

in this paper, we apply the local fractional adomian decomposition and variational iteration methods to obtain the analytic approximate solutions of fredholm integral equations of the second kind within local fractional derivative operators. the iteration procedure is based on local fractional derivative. the obtained results reveal that the proposed methods are very efficient and simple tools ...

In this paper, we consider the variable-order nonlinear fractional diffusion equation ∂u(x, t) ∂t = B(x, t)xR u(x, t) + f(u, x, t), where xR α(x,t) is a generalized Riesz fractional derivative of variable order α(x, t) (1 < α(x, t) ≤ 2) and the nonlinear reaction term f(u, x, t) satisfies the Lipschitz condition |f(u1, x, t) − f(u2, x, t)| ≤ L|u1 − u2|. A new explicit finite difference approxim...

in this paper, a technique generally known as meshless numerical scheme for solving fractional dierential equations isconsidered. we approximate the exact solution by use of radial basis function(rbf) collocation method. this techniqueplays an important role to reduce a fractional dierential equation to a system of equations. the numerical results demonstrate the accuracy and ability of this me...