Numerical simulation for fractional-order differential system of a Glioblastoma Multiforme and Immune system

Advances in Difference Equations

M. A. Abdelkawy¹  M. M. Al-Shomrani² 

[1] Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt;Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia;Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia;

关键词: Spectral collocation method;    Gauss–Radau quadrature;    Shifted Legendre polynomials;    Caputo fractional derivative;    Glioblastoma multiforme;    Immune system;    65M70;    41A55;    26A33;   

DOI  :  10.1186/s13662-020-02978-2

来源: Springer

【 摘 要 】

In this paper, we present a numerical simulation to study a fractional-order differential system of a glioblastoma multiforme and immune system. This numerical simulation is based on spectral collocation method for tackling the fractional-order differential system of a glioblastoma multiforme and immune system. We introduce new shifted fractional-order Legendre orthogonal functions outputted by Legendre polynomials. Also, we state and derive some corollaries and theorems related to the new shifted fractional order Legendre orthogonal functions. The shifted fractional-order Legendre–Gauss–Radau collocation method is developed to approximate the fractional-order differential system of a glioblastoma multiforme and immune system. The basis of the shifted fractional-order Legendre orthogonal functions is adapted for temporal discretization. The solution of such an equation is approximated as a truncated series of shifted fractional-order Legendre orthogonal functions for temporal variable, and then we evaluate the residuals of the mentioned problem at the shifted fractionalorder Legendre–Gauss–Radau quadrature points. The accuracy of the novel method is demonstrated with several test problems.

【 授权许可】

CC BY