带一般积分变换的残差幂级数法的通用系数公式
Universal Coefficients Formula for the Residual Power Series Method with General Integral Transform
AI总结：
本文针对残差幂级数法求解时间分数阶微分方程时系数计算代价高的问题，提出基于一般积分变换的通用系数显式公式，消除重复计算并兼容类拉普拉斯变换的各种RPS变体。
摘要：
本文提出了一种新方法，用于解决残差幂级数（RPS）方法及其采用类拉普拉斯变换的变体在求解时间分数阶微分方程时的固有局限性。现有方法虽然有效，但通常需要对级数解的系数进行计算代价高昂的运算。为克服这一局限，我们提出了一种利用一般积分变换的RPS方法新框架。该框架引入了计算系数的显式公式，从而消除了重复计算并简化了求解过程。此外，它提供了一种普遍适用的方法，与采用类拉普拉斯变换变体的各种RPS方法保持兼容。
英文摘要：
This paper introduces a novel approach to address inherent limitations in the Residual Power Series (RPS) method and its variants with Laplace-like transforms when applied to solving time-fractional differential equations. Existing methods, while successful, often require computationally expensive calculations for the coefficients of the series solution. To overcome this limitation, we propose a new framework for the RPS method that utilizes a general integral transform. This framework incorporates an explicit formula for calculating coefficients, thereby eliminating repetitive computations and streamlining the solution process. Moreover, it offers a universally applicable approach, remaining compatible with various RPS methods that employ Laplace-like transform variants.
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