The aim of this paper is a new semianalytical technique called the variational iteration transform method for solving fractional-order diffusion equations. In the variational iteration technique, identifying of the Lagrange multiplier is an essential rule, and variational theory is commonly used for this purpose. The current technique has the edge over other methods as it does not need extra parameters and polynomials. The validity of the proposed method is verified by considering some numerical problems. The solution achieved has shown that the better accuracy of the proposed technique. This paper proposes a simpler method to calculate the multiplier using the Shehu transformation, making a valuable technique to researchers dealing with various linear and nonlinear problems.

中文翻译：

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分数阶时变扩散方程的数值分析

本文的目的是一种新的半分析技术，称为变分迭代变换方法，用于求解分数阶扩散方程。在变分迭代技术中，确定拉格朗日乘数是必不可少的规则，而变分理论通常用于此目的。当前的技术比其他方法更具优势，因为它不需要额外的参数和多项式。通过考虑一些数值问题，验证了该方法的有效性。所获得的解决方案表明，所提出的技术具有更好的准确性。本文提出了一种使用Shehu变换来计算乘数的简单方法，这为研究各种线性和非线性问题的研究人员提供了一种有价值的技术。