Abstract In this article, exact solutions of some Laplace-type fractional boundary value problems (FBVPs) are investigated via natural decomposition method. The fractional derivatives are described within Caputo operator. The natural decomposition technique is applied for the first time to boundary value problems (BVPs) and found to be an excellent tool to solve the suggested problems. The graphical representation of the exact and derived results is presented to show the reliability of the suggested technique. The present study is mainly concerned with the approximate analytical solutions of some FBVPs. Moreover, the solution graphs have shown that the actual and approximate solutions are very closed to each other. The comparison of the proposed and variational iteration methods is done for integer-order problems. The comparison, support strong relationship between the results of the suggested techniques. The overall analysis and the results obtained have confirmed the effectiveness and the simple procedure of natural decomposition technique for obtaining the solution of BVPs.

中文翻译：

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拉普拉斯分数边值问题的自然分解法精确解

摘要 本文通过自然分解方法研究了一些拉普拉斯型分数边值问题(FBVPs)的精确解。分数导数在 Caputo 算子中描述。自然分解技术首次应用于边值问题 (BVP)，并发现它是解决建议问题的绝佳工具。提供了精确和导出结果的图形表示，以显示所建议技术的可靠性。本研究主要关注一些 FBVP 的近似解析解。此外，解图显示实际解和近似解彼此非常接近。针对整数阶问题对所提出的迭代方法和变分迭代方法进行了比较。比较，支持建议技术的结果之间的密切关系。整体分析和所得结果证实了自然分解技术获得BVPs解的有效性和简单的程序。