In this article, we investigate the semi-analytic solutions of non-linear Volterra fractional integro-differential equations by using Laplace Adomian decomposition method. We discuss the method in general and provide examples for the illustration purpose. Moreover, we give existence and uniqueness result for the solutions using Banach contraction principle as tool. Also we provide some results for the convergence of Laplace Adomian decomposition technique. The results in this work show that the method of Laplace Adomian decomposition is an effective tool for the solutions of Volterra fractional integro-differential equations.

中文翻译：

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非线性Volterra分式积分微分方程的存在理论和半分析研究。

在本文中，我们使用Laplace Adomian分解方法研究了非线性Volterra分式积分微分方程的半解析解。我们通常讨论该方法，并提供示例用于说明目的。此外，我们以Banach压缩原理为工具给出了解的存在性和唯一性结果。同样，我们为拉普拉斯阿德曼分解技术的收敛性提供了一些结果。这项工作的结果表明，拉普拉斯Adomian分解方法是解决Volterra分数阶积分微分方程的有效工具。