One of the basic hydrodynamic models is the famous Burgers formula. This describes the creation of the sticky particle velocity field which interacts only when it collides. In the present paper, we are going to give a systematic formulation of a new family of Burgers-like equations with fractional space–time order. Exact solutions are constructed by using the direct method. A geometrical study for the fractional space is presented and applied to the obtained solutions. The present solutions are the same as the integer one and revealed that the arbitrariness of fraction orders makes systems even richer.

中文翻译：

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分数阶时空类汉堡方程族的几何研究及解

其中 的 的 基本 流体力学 模型 是 在 著名的汉堡 配方。此 描述 创建 的 粘 颗粒 速度 场 ，其 相互作用 仅 当 它 碰撞。在本文中，我们将给出具有分数时空顺序的类 Burgers 方程族的系统公式。使用直接方法构造精确解。提出了分数空间的几何研究并将其应用于获得的解决方案。目前的解决方案与整数一相同，并揭示了分数阶的任意性使系统更加丰富。