Herein, we adduce, analyze, and come up with spectral collocation procedures to iron out a
specific class of nonlinear singular Lane–Emden (LE) equations with generalized Caputo …

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 …

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 this research paper, we address the time-fractional heat conduction equation in one
spatial dimension, subject to nonlocal conditions in the temporal domain. To tackle this …

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 …

The homotopy perturbation method is extend to derive the approximate solution of the
variable order fractional partial differential equations with time delay. The variable order …

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 …

The Allee effect and harvesting always get a pivotal role in studying the preservation of a
population. In this context, we consider a Caputo fractional-order logistic model with the …

This article proposes an efficient simulation to investigate the fractal-fractional (FF) pollution
model's solution behavior for a network of three lakes connected by channels. With the aid of …