In this research, we present a new computational technique for solving some physics
problems involving fractional-order differential equations including the famous Bagley …

Herein, a pure shifted Jacobi–Galerkin (SJG) method is offered for handling linear two-
dimensional space-time diffusion and telegraph equations but by considering their …

In this paper, we apply the Bernstein collocation method to construct the solution set of the
Sylvester matrix differential equation (Sy-MDE) which involves the Lyapunov matrix …

This paper describes an algorithm for obtaining approximate solutions to a variety of well-
known Lane-Emden type equations. The algorithm expands the desired solution y (x)≃ y N …

Herein, modified orthogonal polynomials are introduced. These polynomials are generated
from the second kind of shifted Chebyshev polynomials on the interval [α, β]. The operational …

A new form of basis functions structures has been constructed. These basis functions
constitute a mix of Chebyshev polynomials and Legendre polynomials. The main purpose of …

This research work aims to theoretically examine the influence of various factors on the three-
dimensional nanofluid flow. The study includes parameters such as temperature ratio …

This paper presents a numerical procedure for handling delay fractional differential
problems where the derivative is defined using the M-fractional approach. The proposed …

In this work, the tempered fractional derivative in the Caputo form is considered to define the
tempered time fractional coupled Burger's equations. The Chebyshev polynomials, as a well …

In this paper, we present the general Bernstein functions for the first time. The properties of
generalized Bernstein basis functions are given and demonstrated. The classical Bernstein …