Purpose

The purpose of this paper is to find approximate solutions for a general class of fractional order boundary value problems that arise in engineering applications.

Design/methodology/approach

A newly developed semi-analytical scheme will be applied to find approximate solutions for fractional order boundary value problems. The technique is regarded as an extension of the well-established variation iteration method, which was originally proposed for initial value problems, to cover a class of boundary value problems.

Findings

It has been demonstrated that the method yields approximations that are extremely accurate and have uniform distributions of error throughout their domain. The numerical examples confirm the method’s validity and relatively fast convergence.

Originality/value

The generalized variational iteration method that is presented in this study is a novel strategy that can handle fractional boundary value problem more effectively than the classical variational iteration method, which was designed for initial value problems.

中文翻译：

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工程应用中遇到的分数阶 BVP 的扩展变分迭代法

目的

本文的目的是为工程应用中出现的一类一般的分数阶边值问题寻找近似解。

设计/方法/途径

将应用新开发的半解析方案来寻找分数阶边值问题的近似解。该技术被认为是完善的变分迭代方法的扩展，该方法最初是为初始值问题提出的，以涵盖一类边界值问题。

发现

已经证明，该方法产生的近似值非常准确，并且在整个域中具有均匀的误差分布。数值例子证实了该方法的有效性和相对较快的收敛性。

原创性/价值

本研究提出的广义变分迭代法是一种新策略，可以比针对初值问题设计的经典变分迭代法更有效地处理分数边值问题。