Herein, we offer semi− analytic numerical procedures for the 1− D Tricomi− type time−
fractional equation (T− FTTE). We consider the Jacobi− shifted polynomials as basis …

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 …

A Numerical solution of the Caputo-time and Riesz-space fractional reaction–diffusion
model is considered in this paper. Based on finite difference schemes, we formulate both …

This study offers a novel method for solving the partial differential equation known as the
time-fractional Newell-Whitehead-Segel equation (TFNWSE), which has important …

This article is dedicated to propose a spectral solution for the non-linear Fitzhugh–Nagumo
equation. The proposed solution is expressed as a double sum of basis functions that are …

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 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 …

Herein, we construct an explicit modal numerical solver based on the spec-tral Petrov–
Galerkin method via a specific combination of shifted Cheby-shev polynomial basis for …

This paper presents a numerical strategy for solving the nonlinear time fractional Burgers's
equation (TFBE) to obtain approximate solutions of TFBE. During this procedure, the …

This paper employs a numerical method for the numerical treatment of the time fractional
Fokker–Planck equation. This method is based on applying the spectral Petrov–Galerkin …