Abstract

For a fractional ordinary differential equation, we consider a problem where the boundary conditions are given in the form of linear functionals. This permits covering a fairly broad class of linear local and nonlocal conditions. The fractional derivative is understood in the sense of Gerasimov–Caputo. A necessary and sufficient condition for the unique solvability of the problem is obtained. A representation of the solution via special functions is found. A theorem on the existence and uniqueness of the solution is proved.

中文翻译：

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分数常微分方程的奈马克问题

摘要

对于分数常微分方程，我们考虑边界条件以线性函数形式给出的问题。这允许覆盖相当广泛的线性局部和非局部条件。分数阶导数是按照格拉西莫夫-卡普托的意义来理解的。得到问题唯一可解的充要条件。通过特殊函数找到解决方案的表示。证明了解的存在性和唯一性定理。