论文标题
$ l^p $ - 空间中的分数衍生物和时间折叠的普通微分方程
Fractional derivatives and time-fractional ordinary differential equations in $L^p$-space
论文作者
论文摘要
我们通过操作员理论定义了基于$ l^p（0，t）$的Sobolev空间中的分数衍生物$ \ pppa $，并表征了Sobolev-Slobodecki Spaces $ W^{α，P}（α，P}（0，T）$的$ \ pppa $的域。此外，我们将$ \ pppa u $定义为$ u \ in l^p（0，t）$中的$ u \。然后，我们通过这种$ \ pppa $讨论线性分数普通微分方程的初始值问题，并根据系数的规律性和方程式中的非均匀项，建立了有关指定类中唯一解决方案的独特存在的结果。
We define fractional derivatives $\pppa$ in Sobolev spaces based on $L^p(0,T)$ by an operator theory, and characterize the domain of $\pppa$ in subspaces of the Sobolev-Slobodecki spaces $W^{α,p}(0,T)$. Moreover we define $\pppa u$ for $u\in L^p(0,T)$ in a sense of distribution. Then we discuss initial value problems for linear fractional ordinary differential equations by means of such $\pppa$ and establish several results on the unique existence of solutions within specified classes according to the regularity of the coefficients and the non-homogeneous terms in the equations.
