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 …

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 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 …

We provide here a novel approach for solving IVPs in ODEs and MTFDEs numerically by
means of a class of MSJPs. Using the SCM, we build OMs for RIs and RLFI for MSJPs as …

On Linearization Coefficients of Shifted Jacobi Polynomials Page 1 Contemporary Mathematics
http://ojs.wiserpub.com/index.php/CM/ Research Article On Linearization Coefficients of Shifted …

In the present paper, we construct a set of multiscale orthonormal basis based on Legendre
polynomials. Using this orthonormal basis, a new algorithm is designed for solving the …

This paper presents a numerical scheme for solving the non-linear time fractional Klein-
Gordon equation. To approximate spatial derivatives, we employ the pseudo-spectral …

In this paper, we demonstrate the local well-posedness and blow up of solutions for a class
of time-and space-fractional diffusion wave equation in a fractional power space associated …

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 …