An algorithm for approximating solutions to fractional differential equations (FDEs) in a
modified new Bernstein polynomial basis is introduced. Writing x→ x α (0< α< 1) in the …

This study introduces a new fractional order Fibonacci wavelet technique proposed for
solving the fractional Bagley-Torvik equation (BTE), along with the block pulse functions. To …

The principal aim of the current paper is to present and analyze two new spectral algorithms
for solving some types of linear and nonlinear fractional-order differential equations. The …

In this study, we propose shifted fractional-order Jacobi orthogonal functions (SFJFs) based
on the definition of the classical Jacobi polynomials. We derive a new formula that explicitly …

In this paper, a potentially useful new method based on the Gegenbauer wavelet expansion,
together with operational matrices of fractional integral and block-pulse functions, is …

In this article, a new method is generated to solve nonlinear Lane–Emden type equations
using Legendre, Hermite and Laguerre wavelets. We are interested to note that these …

This article is interested in presenting and implementing two new numerical algorithms for
solving multi-term fractional differential equations. The idea behind the proposed algorithms …

In this paper, we develop a precise and efficient ultraspherical wavelet method for a famous
Benjamin-Bona-Mahony (BBM) mathematical model. The suggested technique uses the …

Herein, two numerical algorithms for solving some linear and nonlinear fractional-order
differential equations are presented and analyzed. For this purpose, a novel operational …

A numerical algorithm for solving multi-term fractional differential equations (FDEs) is
established herein. We established and validated an operational matrix of fractional …