A new modified definition of Caputo-Fabrizio fractional-order derivative and their applications to the Multi Step Homotopy Analysis Method (MHAM)
A new modified definition of Caputo-Fabrizio fractional-order derivative and their applications to the Multi Step Homotopy Analysis Method (MHAM)
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DOI：
10.1016/j.cam.2018.07.023
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发表时间：
2019-01
期刊：
影响因子：
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通讯作者：
H. Yépez-Martínez;J. F. Gómez‐Aguilar
中科院分区：
文献类型：
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作者：
H. Yépez-Martínez;J. F. Gómez‐Aguilar
本文在Caputo-Fabrizio分数阶算子的基础上给出了一种新的具有光滑核的分数阶导数的定义，该定义考虑了传统的Caputo-Fabrizio分数阶导数定义所存在的一些问题.本文介绍的Modified-Caputo-Fabrizio分数阶导数在用某些近似解析方法求解非线性分数阶微分方程时具有一定的优越性。我们考虑两种近似的解析方法来找到这个新的运营商的解析解同伦分析方法（HAM）和多步同伦分析方法（MHAM）。所获得的结果表明，引入修改后的Caputo-Fabrizio分数阶导数可以在未来应用于分数动力学的许多不同的场景。
In this paper, we present a new definition of fractional-order derivative with a smooth kernel based on the Caputo–Fabrizio fractional-order operator which takes into account some problems related with the conventional Caputo–Fabrizio factional-order derivative definition. The Modified-Caputo–Fabrizio fractional-order derivative here introduced presents some advantages when some approximated analytical methods are applied to solve non-linear fractional differential equations. We consider two approximated analytical methods to find analytical solutions for this novel operator; the homotopy analysis method (HAM) and the multi step homotopy analysis method (MHAM). The results obtained suggest that the introduction of the Modified-Caputo–Fabrizio fractional-order derivative can be applied in the future to many different scenarios in fractional dynamics.