The motivation of this paper is to construct the solution of fractional partial differential equations (FPDEs) by the combination of Laplace transform homotopy analysis method (LHAM) and the Laplace transform residual power series method (LRPSM) with weighted Atangana-Baleanu and weighted Caputo-Fabrizio fractional derivatives with specific weighted functions. Moreover, the solutions are analyzed by comparing with exact solutions of these equations. The obtained consequences illustrate that methods LHAM and LRPSM work very well to determine the solutions of FPDEs with weighted fractional derivatives in consideration.

中文翻译：

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加权分数算子对分数阶偏微分方程的求解

本文的目的是通过结合拉普拉斯变换同伦分析方法（LHAM）和拉普拉斯变换残差幂级数方法（LRPSM）并结合加权Atangana-Baleanu和加权Caputo-n，构造分数阶偏微分方程（FPDE）的解决方案具有特定加权功能的Fabrizio小数衍生物。此外，通过与这些方程式的精确解进行比较来分析解。所获得的结果表明，LHAM和LRPSM方法可以很好地确定考虑了加权分数导数的FPDE的解。