This paper presents a novel hybrid technique which is developed by incorporating the fractional derivatives in the generalised integral transform method. Homotopy analysis method is combined with fractional generalised integral transform method to solve the fractional order nonlinear differential equations. The performance of the proposed method is analysed by solving various categories of nonlinear fractional differential equations like Navier Stokes’s model and Riccatti equations, etc. Unlike the other analytical methods, the hybrid method provides a better way to control the convergence region of the obtained series solution through an auxiliary parameter h. Furthermore, as proposed in this paper, the ‘Fractional Generalised Homotopy Analysis Method’ along with the several examples reveal that this method can be effectively used as a tool for solving various kinds of nonlinear fractional differential equations.

中文翻译：

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求解非线性分数阶微分方程的分数阶广义同伦分析方法

本文提出了一种新的混合技​​术，该技术是通过将分数导数并入广义积分变换方法中而开发的。同伦分析方法与分数阶广义积分变换方法相结合，求解分数阶非线性微分方程。通过求解各种类型的非线性分数阶微分方程，例如Navier Stokes模型和Riccatti方程等，分析了该方法的性能。与其他分析方法不同，混合方法提供了一种更好的方法来控制所获得级数解的收敛区域通过辅助参数h。此外，如本文所提出的，“分数次广义同伦分析方法”以及几个示例表明，该方法可以有效地用作求解各种非线性分数阶微分方程的工具。