In this study, we present an innovative approach involving a spectral collocation algorithm to
effectively obtain numerical solutions of the nonlinear time-fractional generalized Kawahara …

This paper investigates the well-posedness of a class of FSIDEs utilizing the fractional
Caputo–Fabrizio derivative. Herein, the well-posedness proofs are constructed by …

The pseudo-spectral method is used as a technique to employ the first derivative of the well-
known Legendre polynomials (FDLs) as novel basis functions. Then, the FDLs Gauss …

This paper considers linear and nonlinear fractional delay Volterra integrodifferential
equation of order ρ in the Atangana–Beleanu–Caputo (ABC) sense. We used continuous …

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 …

This paper will present a highly efficient technique for solving linear and nonlinear
differential equations. We will use the second derivative of Legendre polynomials as new …

Legendre polynomials' first derivatives have been used as the basis function via the pseudo-
Galerkin spectral method. Operational matrices for derivatives have been used and …

The main aim of this paper is to introduce a new class of orthogonal polynomials that
generalizes the class of Chebyshev polynomials of the first kind. Some basic properties of …

This paper investigates a highly efficient method that depends on the Tau method for solving
initial and boundary value problems. The second derivatives of Legendre polynomials …

This paper presents a new method to numerically solve the nonlinear time-fractional
generalized Kawahara equations (NTFGKE) with uniform initial boundary conditions (IBCs) …