An efficient numerical method for fractional order nonlinear two-point boundary value problem occurring in chemical reactor theory

Abstract

This paper is focused on computing an approximate numerical solution of the strongly nonlinear multi-order fractional version (SNMOFV) of a BVP that appears in the theory of chemical reactors. The fractional derivative is defined by using Caputo’s methodology. This research article present a numerical method based upon collocation method with Laguerre polynomials (LPs) and Vieta–Lukas polynomials (VLPs) for the considered problem. This method’s key benefit is the excellent precision and user-friendly approach that are obtained from a limited number of Laguerre and Vieta–Lukas polynomials. Basically, in this article, we offer the numerical solution of the considered fraction model by using the Laguerre collocation technique (LCT) and the Vieta–Lukas collocation technique (VLCT). Also, we present a comparison of the collocation technique with the generalized differential transform method (GDTM). Error analysis of LCT and VLCT is also presented in this paper.

Keywords

• Fractional boundary value problem
• Laguerre polynomials
• Vieta–Lukas polynomials
• Collocation technique
• Caputo fractional derivative