分数阶算子探讨

简要介绍了用以描述物理和力学中的中间过程(intermediate processes)和临界现象(critical phenomena)的分数阶算子理论、方法的最新进展。分析了分数阶算子对湍流速度场的不规则起伏、Brown运动和粘弹性材料记忆性等经典力学和线性物理问题的挑战。总结了分数阶算子在线性和非线性固体遗传动力学、非Newton流体力学、生物物理和生物力学、分数阶反常扩散与随机游走理论和DLA理论等复杂系统中的应用。包括了作者近年来在这一领域所做的工作。最后,对这一学科的发展进行了展望。

Theory and Method of Fractional Operator and its Applications to the Modern Mechanics

Theory and method of fractional operator which is used to describe intermediate processes and critical phenomena in physics and its applications to the modern mechanics were introduced in this paper.It was pointed that the problems of classical mechanics and linear physics,such as stochastic fluctuation of turbulence velocity fields,Brown motion,memory of viscoelastic material,face the challenge of fractional operator.Applications of fractional operator in complex systems,which include solid heredity dynamics,non-Newtonian fluid mechanics,biophysics and biomechanics,fractional anomalous diffusion,stochastic walk theory and DLA theory,were discussed.The authors' researches on this area were introduced,and prospects of the subject were forecasted finally.