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1·A novel fuzzy fractional order proportional integral derivative (FFPID) controller based on fractional calculus is presented.

在分析分数阶微积分的基础上，提出了一种新型模糊分数阶比例积分微分控制器。

2·Under the Euclidean measure, the analytical solutions to the above problem are obtained by employing the Riemann Liouville fractional calculus theory.

在欧氏测度下 ，应用R L分数阶微积分算子理论给出了上述问题的精确解 。

3·Fractional calculus is related to fractal, in particular is closely linked with the fractal function, which is a powerful tool to study the fractal function.

分数阶微积分与分形，特别是分形函数紧密相连，是研究分形函数的一个有力工具。

4·On the basis of the fractional calculus operator theory, the stress-strain relation of soft soil under the condition of loading with constant strain rate is proposed.

利用分数阶微积分理论提出等应变率加载情况下的软土应力—应变关系。关系式显示应力—应变之间呈乘幂函数关系。

5·Within the framework of the fractional calculus theory, the mechanism of fractal dynamics is introduced to the constitutive equation research of viscoelastic materials.

在分数阶微积分的理论框架下，将分形动力学的机制引入到生物黏弹性本构方程的研究中。

6·Fractional Hall effect is described in an universal formalized theory of fraction-dimension calculus. The three existence theorems of the fractional infinite product state are given.

给予分数Hall效应以普遍的分数微积分数学形式理论描述。并给出无穷积态存在三条定理。