In this paper, a new alternating direction implicit Galerkin–Legendre spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed. The temporal component is discretized by the Crank–Nicolson method. The detailed implementation of the method is presented. The stability and convergence analysis is strictly proven, which shows that the derived ...

In this paper, we construct and analyze a linearized finite difference/Galerkin–Legendre spectral scheme for the nonlinear multiterm Caputo time fractional-order reaction-diffusion equation with delay Riesz space fractional derivatives. The temporal orders in considered model are taken as 0 <m...

The principle result of this paper is the following operational Tau method based upon Müntz-Legendre polynomials. This methodology provides a computational technique for numerical solution of fractional differential equations by using a sequence of matrix operations. The main property of Müntz polynomials is that fractional derivatives of these polynomials can be expressed in terms of the same ...

Models of bio-mathematics are experimental systems that recreate aspects human tissue function, diseases or virus. In this research, a new operational matrix based on the Laguerre wavelets is introduced for arbitrary-order susceptible-infected-recovered (SIR) epidemic dynamical system childhood diseases. An exact mechanism Riemann–Liouville arbitrary integral operator explained where derivative...

In this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the Laplacian equation. Themethod is based on the use of the Galerkin method with CAS wavelets constructed on the unit interval as basis.This approach utilizes the non-uniform Gauss-Legendre quadrature rule for ...

Fractional derivative models involving generalized Mittag-Leffler kernels and opposing are investigated. We first replace the classical with GMLK in order to obtain new fractional-order (GMLK) three parameters that utilize a spectral collocation method based on Legendre’s polynomials for evaluating numerical solutions of pr. then construct scheme by using Legendre polynomials. In model, we dire...

The Legendre multiwavelet Galerkin method is adopted to give the approximate solution for the nonlinear fractional partial differential equations (NFPDEs). The Legendre multiwavelet properties are presented. The main characteristic of this approach is using these properties together with the Galerkin method to reduce the NFPDEs to the solution of nonlinear system of algebraic equations.We prese...

To solve fractional delay differential equation systems, the Laguerre Wavelets Method (LWM) is presented and coupled with steps method in this article. Caputo derivative used proposed technique. The results show that current procedure accurate reliable. Different nonlinear systems have been solved, compared to exact solution different methods. Furthermore, it clear from figures LWM error conver...

The mollification obtained by truncating the expansion in wavelets is studied, where the wavelets are so chosen that noise is reduced and the Gibbs phenomenon does not occur. The estimations of the error of approximation of the mollification are given for the case when the fractional derivative of a function is calculated. Noting that the estimations are applicable even when the orthogonality o...