In this article a new approach in solving time fractional partial differential equations is introduced, that is, the ARA-residual power series method. The main idea of this technique, depends on applying the ARA-transform and using Taylor's expansion to construct approximate series solutions. The procedure of getting the approximate solutions for nonlinear time fractional partial differential equations is a difficult mission, the ARA-residual power series method over comes this trouble throughout expressing the solution in a series form then obtain the series coefficients using the idea of the residual function and the concept of the limit at infinity. This method is efficient and applicable to solve a wide family of time fractional partial differential equations. Four attractive applications are considered to show the speed and the strength of the proposed method in constructing solitary series solutions of the target equations.

翻译：本文提出了一种求解时间分数阶偏微分方程的新方法，即ARA-残差幂级数法。该方法的核心思想依赖于应用ARA变换并结合泰勒展开来构造近似级数解。对于非线性时间分数阶偏微分方程，求解近似解的过程是一项艰巨任务，而ARA-残差幂级数法通过将解表达为级数形式，然后利用残差函数概念和无穷极限思想求解级数系数，从而克服了这一困难。该方法高效且适用于求解一大类时间分数阶偏微分方程。通过四个典型应用实例，展示了所提方法在构建目标方程孤立波级数解方面的快速性和有效性。