We present a fractional series solution (FSS) for a class of higher-order linear fractional PDEs. The fractional derivative in this class is considered in the conformable fractional derivative (Co-FD) sense. An appropriate expansion was introduced to reach an FSS that is consistent with the target equations in this research. The residual power series technique is used to determine the coefficients of the FSS. Five applications are tested to verify the effectiveness of the used method, as well as to compare the current results with the previous results for the same applications in which the fractional derivative was considered in the Caputo sense. Numerical and graphical comparisons are made to determine the compatibility of the behavior of the solution in the case of the use of the concept of Co-FD as a suitable alternative to the use of the concept of Caputo fractional derivative (Ca-FD) in the modeling of natural phenomena.

我们为一类高阶线性分数阶偏微分方程提供分数级数解（FSS）。从一致性分数导数（Co-FD）的意义上考虑此类中的分数导数。引入了适当的扩展以达到与本研究中的目标方程式一致的FSS。剩余功率序列技术用于确定FSS的系数。测试了五个应用程序，以验证所使用方法的有效性，并将当前结果与以前在Caputo意义上考虑分数导数的相同应用程序的结果进行比较。