Abstract In this article, analytical exact and approximate solutions for fractional physical equations are obtained successfully via efficient analytical method called fractional residual power series method (FRPSM). The fractional derivatives are described in the Caputo sense. Three applications are discussed, showing the validity, accuracy and efficiency of the present method. The solution via FRPSM shows excellent agreement in comparison with the solutions obtained from other established methods. Also, the FRPSM can be used to solve other nonlinear fractional partial differential equation problems. The final results are presented in graphs and tables, which show the effectiveness, quality and strength of the presented method.

中文翻译：

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用于分数物理现象的分析和近似研究的分数剩余幂级数方法

摘要 在本文中，通过称为分数剩余幂级数法（FRPSM）的高效解析方法，成功地获得了分数物理方程的解析精确解和近似解。分数导数是在 Caputo 意义上描述的。讨论了三个应用，显示了本方法的有效性、准确性和效率。与从其他既定方法获得的解决方案相比，通过 FRPSM 获得的解决方案显示出极好的一致性。此外，FRPSM 还可用于求解其他非线性分数阶偏微分方程问题。最终结果以图形和表格的形式呈现，显示了所提出方法的有效性、质量和强度。