摘要
从初等函数eax和xp的整数阶微积分入手,探索函数的分数阶微积分形式,并给出其级数形式.通过与经典分数阶微积分的定义比较,给出了不同定义下简单函数f(t)=t的1/2阶微积分.结果表明,同一函数在不同定义形式下的分数阶微积分相差一个上限为分数的级数.
Starting from the integral calculus of functions e~ and xp , we study the form of the fractional calculus of elemerltary functions, and some series forms of the fractional calculus of the functions are given. Comparing with the definition of classical fractional calculus, we calculate the 1/2 order calculus of the simple functions f（t）=t in the different definitions. The results show that the fractional calculus of the same function in different definitions are different in the series which upper limit is a fraction.
出处
《内蒙古师范大学学报（自然科学汉文版）》
CAS
北大核心
2017年第4期479-482,共4页
Journal of Inner Mongolia Normal University(Natural Science Edition)
基金
国家自然科学基金资助项目(11262017)
内蒙古师范大学"十百千人才工程"研究项目(RCPY-2-2012-K-035)
内蒙古师范大学重大培育专项基金项目(2014ZD03)
