Computer Science ›› 2016, Vol. 43 ›› Issue (3): 23-26.

### Formalization of Consistency of Fractional Calculus in HOL4

LI Shan-shan, ZHAO Chun-na, GUAN Yong, SHI Zhi-ping, WANG Rui, LI Xiao-juan and YE Shi-wei

• Online:2018-12-01 Published:2018-12-01

Abstract: Fractional calculus has three commonly used definitions,including Grunwald-Letnikov,Riemann-Liouville and Caputo definition.There are connections among these three kinds of definitions.They are interchangeable under certain conditions.This paper established a formal model of fractional calculus based on Caputo definition in the higher-order logic proof tool HOL4 using real,integral,limitation and transcendental functions.In order to achieve the conversion of these three definitions in HOL4,we verified the relationships among Caputo,Grunwald-Letnikov and Riemann-Liouville definition.This work will make these three definitions unite in a certain extent,and will also perfect the theo-rem library of higher-order logic.

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