用算子方法定义复阶积分和导数
Definitions of complex order integrals and derivatives using operator approach
摘要：
对于复数s，满足一定条件的函数f的s阶积分定义为算子J^s对f的作用。首先给出了复数s具有正实部的情况下算子J^s的定义。然后，利用一阶导数的算子，记为D^1，是算子J^1的左手侧逆的事实，s阶导数算子，记为D^s，也被定义用于具有正实部的所有复数s。最后，考虑关系J^s=D^（-s），将s阶积分和s阶导数的定义推广到所有复数s，并给出了算子定义域的推广。
英文摘要：
For a complex number s, the s-order integral of function f fulfilling some conditions is defined as action of an operator, noted J^s, on f. The definition of the operator J^s is given firstly for the case of complex number s with positive real part. Then, using the fact that the operator of one order derivative, noted D^1, is the left- hand side inverse of the operator J^1, an s-order derivative operator, noted D^s, is also defined for all complex number s with positive real part. Finally, considering the relation J^s=D^(-s), the definition of the s-order integral and s-order derivative is extended for all complex number s.An extension of the definition domain of the operators is given too.
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