Shifted Jacobi polynomials for nonlinear singular variable-order time fractional Emden–Fowler equation generated by derivative with non-singular kernel

Advances in Difference Equations

Z. Avazzadeh¹  M. H. Heydari²  A. Atangana³ 

[1] Department of Applied Mathematics, Xi’an Jiaotong-Liverpool University, 215123, Suzhou, Jiangsu, China;Department of Mathematics, Shiraz University of Technology, Shiraz, Iran;Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South Africa;Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan;

关键词: Shifted Jacobi polynomials (SJPs);    Operational matrices;    Variable-order (VO) time fractional derivative;    Singular VO time fractional Emden–Fowler equation;   

DOI  :  10.1186/s13662-021-03349-1

来源: Springer

【 摘 要 】

In this work, a nonlinear singular variable-order fractional Emden–Fowler equation involved with derivative with non-singular kernel (in the Atangana–Baleanu–Caputo type) is introduced and a computational method is proposed for its numerical solution. The desired method is established upon the shifted Jacobi polynomials and their operational matrix of variable-order fractional differentiation (which is extracted in the present study) together with the spectral collocation method. The presented method transforms obtaining the solution of the main problem into obtaining the solution of an algebraic system of equations. Several numerical examples are examined to show the validity and the high accuracy of the established method.

【 授权许可】

CC BY