Abstract: In this paper we consider a kind of polynomials-Legendre polynomials then we get Legendre wavelet. Legendre wavelet operational matrix of the fractional integration is derived and combined ...

This project focuses on solving Bessel's and Legendre's differential equations using Physics-Informed Neural Networks (PINN). By integrating domain knowledge directly into the neural network, we ...

The unnormalized Legendre function is a solution to the Legendre differential equation, which is commonly used in problems involving spherical symmetry, such as gravitational and electrostatic ...

1 Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, KSA 2 Department of Mathematics, Faculty of Science, Benha University, ...

The various types of special functions have become essential tools for scientists and engineers. One of the important classes of special functions is of the hypergeometric type. It includes all ...

A note on the generalized and universal associated Legendre equations Citation: Kirk, K. L. A. , Bryenton, K. R. , & Saad, N. . (2018). A note on the generalized and universal associated Legendre ...

Abstract: This paper contributes an efficient numerical approach for solving optimal control problems governed by nonlinear Volterra integral equations. The technique is based upon orthogonal Legendre ...

This research presents a numerical approach to obtain the approximate solution of the n-dimensional co-homological equations of fractional order in continuous-time dynamical systems. For this purpose, ...

We tested different optical elements placed in three different positions by applying the irradiance transport equation (ITE), obtaining the wavefront $[ W(x,y) ]$[W(x ...

Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, KSA; Department of Mathematics, Faculty of Science, Benha University, Benha, ...