摘要
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.
出处
《天津师范大学学报(自然科学版)》
CAS
2016年第5期20-22,共3页
Journal of Tianjin Normal University:Natural Science Edition
基金
吕梁学院自然科学青年基金资助项目(ZRXY201306
ZRXY201308)
关键词
整数阶微积分
分数阶微积分
伽马函数
Hadamard积分
integer order differential and integral
fractional order differential and integral
gamma function
Hadamard integral