论文标题
关于某些广义和分数衍生物的基本理论
On the basic theory of some generalized and fractional derivatives
论文作者
论文摘要
我们继续开发\ cite {jpa}中引入的广义衍生物的基本理论，并提供了一些应用。特别是，我们制定了弱最大原理的版本，罗尔的定理，平均值定理，微积分的基本定理，部分整合部分，以及一个广义的riccati方程的存在和独特定理，每种定理都是构造的，均应以合格的形式衍生的形式，} \ cite {kha}等。最后，我们表明，对于每个$α> 1 $，都有一个分数导数和一个相应的函数，其分数衍生物在实际线上无处不在。
We continue the development of the basic theory of generalized derivatives as introduced in \cite{JPA} and give some of their applications. In particular, we formulate versions of a weak maximum principle, Rolle's theorem, the Mean value theorem, the Fundamental theorem of Calculus, Integration by parts, along with an existence and uniqueness theorem for a generalized Riccati equation, each of which includes, as corollaries, the corresponding version for conformable fractional derivatives considered by \cite{kat}, \cite{kha} among many others. Finally, we show that for each $α> 1$ there is a fractional derivative and a corresponding function whose fractional derivative fails to exist everywhere on the real line.
