一类分数阶微积分的中值定理及应用

The mean value theorem and its applications of a class of fractional calculus

Riemann-Liouville分数阶微积分算子是一类带有一个函数的分数阶微积分算子的特殊情形,以Riemann-Liouville分数阶微积分算子的积分中值定理和微分中值定理为基础,得到了一类带有一个函数的分数阶微积分算子的积分中值定理和微分中值定理,并给出其在计算方面的一些应用。

Riemann-Liouville fractional calculus is a special case of the fractional calculus with respect to another function.Based on mean value theorem of integral and differential mean value theorem of Riemann-Liouville fractional calculus,we got the mean value theorem of integral and differential mean value theorem of the fractional calculus with respect to another function,and given some applications in computation.