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 paper, the existence and uniqueness of a solution to a multi-order fractional nonlinear
evolution equations system are studied by applying Banach's Fixed Point Theorem and …

In this article, we introduce a novel spectral algorithm utilizing Fibonacci polynomials to
numerically solve both linear and nonlinear integro-differential equations with fractional …

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 …

The semi-analytic method based on the Galerkin technique with Chebyshev basis is
presented in this paper to solve the linear integro-differential equations in the Volterra …

In this paper, we explore the numerical analysis of the microscale heat equation. We present
the characteristics of numerical solutions obtained through both semi-and fully-discrete …

In this study, we utilize a specific combination of orthogonal Gegenbauer polynomials as
basis functions that satisfy homogeneous boundary conditions in the spatial variable and …

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 …