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Research Article

A new method of solving the best approximate solution for a nonlinear fractional equation

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Pages 1702-1718 | Received 28 Apr 2022, Accepted 02 May 2023, Published online: 12 Jun 2023
 

Abstract

A new method of solving the best approximate solution for nonlinear fractional equations with smooth and nonsmooth solutions in reproducing kernel space is proposed in the paper. The nonlinear equation outlines some important equations, such as fractional diffusion-wave equation, nonlinear Klein–Gordon equation and time-fractional sine-Gordon equation. By constructing orthonormal bases in reproducing kernel space using Legendre orthonormal polynomials and Jacobi fractional orthonormal polynomials, the best approximate solution is obtained by searching the minimum of residue in the sense of C. Numerical experiments verify that the method has higher accuracy.

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Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Guangdong Basic and Applied Basic Research Foundation [grant no. 2022A1515010022] and GuangDong Ocean University [grant no. R20050].

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