An efficient collocation scheme for new type of variable-order fractional Lane-Emden equation

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 31 مرداد 1403

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.87501.1419

نویسندگان

Hadis Azin^{* 1}؛ Ali Habibirad¹؛ Esmail Hesameddini²؛ Mohammad H. Heydari²

¹Department of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.

²Department of Mathematics, Shiraz University of Technology, Shiraz, Iran.

چکیده

The fractional Lane-Emden model illustrates different phenomena in astrophysics and mathematical physics. This paper involves the Vieta-Lucas (Vt-L) bases to solve types of variable-order (V-O) fractional Lane-Emden equations (linear and nonlinear). The operational matrix of V-O fractional derivative is obtained for the Vt-L polynomials. In the established approach, these polynomials are applied to transform the main problem into an algebraic equations system. To indicate the performance and capability of the scheme, a number of examples are presented for various types of V-O fractional Lane-Emden equations. Also, for one example, a comparison is done between the calculated results by our technique with those obtained via the Bernoulli polynomials. Overall, this paper introduces a new methodology for solving variable-order fractional Lane-Emden equations using Vieta-Lucas bases. The derived operational matrix and the transformation to an algebraic equation system offer practical advantages in solving these equations efficiently. The presented examples and comparative analysis highlight the effectiveness and validity of the proposed technique, contributing to the understanding and advancement of fractional Lane-Emden models in astrophysics and mathematical physics.

کلیدواژه‌ها

Lane-Emden equation؛ Vieta-Lucas polynomials؛ Variable-order fractional differential equation