In this paper, some new nonlinear fractional partial differential equations (PDEs) have been considered.Three models are including the space-time fractional-order Boussinesq equation, space-time (2 + 1)-dimensional breaking soliton equations, and space-time fractional-order SRLW equation describe the behavior of these equations in the diverse applications. Meanwhile, the fractional derivatives in the sense of β -derivative are defined. Some fractional PDEs will convert to the considered ordinary differential equations by the help of transformation of β -derivative. These equations are analyzed utilizing an integration scheme, namely, the extended auxiliary equation mapping method. The different kinds of traveling wave solutions, solitary, topological, dark soliton, periodic, kink, and rational, fall out as a by-product of this scheme. Finally, the existence of the solutions for the constraint conditions is also shown. The outcome indicates that some fractional PDEs are used as a growing finding in the engineering sciences, mathematical physics, and so forth.

中文翻译：

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确定非线性分数阶偏微分方程的新精确孤波解的扩展辅助方程映射方法

本文考虑了一些新的非线性分数阶偏微分方程（PDE），包括时空分数阶Boussinesq方程，时空（2 +1）维破裂孤子方程和时空三种模型。分数阶SRLW方程描述了这些方程在各种应用中的行为。同时，定义了β-导数意义上的分数导数。某些分数阶偏微分方程将借助β导数的变换转换为所考虑的常微分方程。利用积分方案，即扩展辅助方程映射方法，对这些方程进行分析。作为该方案的副产品，各种行波解决方案（孤立的，拓扑的，暗孤子，周期的，扭结的和有理的）落在了一起。最后，还显示了约束条件解的存在性。结果表明，某些分数PDE被用作工程科学，数学物理学等领域的新发现。