Riemann-Liouville和Cputo分数阶微积分

Fractional order differential and integral of Riemann-Liouville and Cputo

利用伽马函数无穷积分探讨了从整数阶微积分到分数阶微积分的过渡和演绎.通过证明整数阶微积分仅是分数阶微积分的一种特殊情况,拓宽了导数和积分的概念.阐述了Riemann-Liouville和Cputo两种不同分数阶导数定义的区别和联系,给出了Hadamard积分与Riemann-Liouville导数之间的关系.

The transition from the integer order differential and integral calculus to the fractional order calculus is discussed by using the gamma function infinite integral. It is proved that the fractional calculus is just a special case of fractional order calculus, and the concept of derivative and integral is broadened. The difference and contact of Riemann Liouville and Cputo fractional derivatives are expounded, and the relation between Hadamard integral and Riemann Liouville derivative is given.