The time-fractional diffusion equation is applied to a wide range of practical applications. We
suggest using a potent spectral approach to solve this equation. These techniques' main …

This paper presents a novel application of the Fractal Fractional derivative to control the flow
of non-Newtonian fluids. The study focuses on the generalized magnetohydrodynamic …

We develop direct solution techniques for solving high-order differential equations with
constant coefficients using the spectral tau method. The spatial approximation is based on …

Herein, we build and implement a combination of Lucas polynomials basis that fulfills the
spatial homogenous boundary conditions. This basis is then used to solve the time-fractional …

In comparison to fractional-order differential equations, integer-order differential equations
generally fail to properly explain a variety of phenomena in numerous branches of science …

The current investigations provides a stochastic platform using the computational Levenberg-
Marquardt Backpropagation (LMB) neural network (NN) approach, ie, LMB-NN for solving …

In this research, a compact combination of Chebyshev polynomials is created and used as a
spatial basis for the time fractional fourth-order Euler–Bernoulli pinned–pinned beam. The …

In this paper, we present an innovative and powerful combination of grammatical evolution
and a physics-informed neural network approach for symbolically solving the Lane-Emden …

This study explores the spectral Galerkin approach to solving the space-time Schrödinger,
wave, Airy, and beam equations. In order to facilitate the creation of a semi-analytical …

In this work, first, a family of fourth‐order methods is proposed to solve nonlinear equations.
The methods satisfy the Kung‐Traub optimality conjecture. By developing the methods into …