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Abstract <p>In this paper, we propose a new method (Bilateral least Squares residual power series method) to solve the Klein–Gordon, KdV, and diffusion equations of space-time fractional derivatives. This method can solve the space-time fractional differential equations that cannot be solved by the classical residual power series method, and can easily complete the operation without using the transformation. It is convenient and fast, and the idea of least squares is used to further reduce the error. Compared with the Bilateral residual power series method, it is more accurate.</p>

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Bilateral Least Squares Residual Power Series Method for Fractional Differential Equations

  • 期刊论文

  • 发表日期：

    2025年7月1日

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  • Chen Liu,
  • Yapeng Shi,
  • Yuqiang Feng,
  • Jun Jiang,
  • Jicheng Yu

摘要

Abstract

In this paper, we propose a new method (Bilateral least Squares residual power series method) to solve the Klein–Gordon, KdV, and diffusion equations of space-time fractional derivatives. This method can solve the space-time fractional differential equations that cannot be solved by the classical residual power series method, and can easily complete the operation without using the transformation. It is convenient and fast, and the idea of least squares is used to further reduce the error. Compared with the Bilateral residual power series method, it is more accurate.