论文标题
分数演算和时间分数微分方程：重新审视和构建理论
Fractional calculus and time-fractional differential equations: revisit and construction of a theory
论文作者
论文摘要
对于分数衍生物和时间分数微分方程，我们基于分数Sobolev空间的操作者理论构建一个框架。我们的框架为经典的Caputo和Riemann-Liouville衍生物提供了可行的扩展，包括分数订单（包括负阶）的Sobolev空间。我们的方法可以实现分数演算和时间分数微分方程的统一处理。我们为分数普通微分方程和分数偏微分方程的初始边界值问题提出初始值问题，以证明拟态性和其他属性。
For fractional derivatives and time-fractional differential equations, we construct a framework on the basis of the operator theory in fractional Sobolev spaces. Our framework provides a feasible extension of the classical Caputo and the Riemann-Liouville derivatives within Sobolev spaces of fractional orders including negative ones. Our approach enables a unified treatment for fractional calculus and time-fractional differential equations. We formulate initial value problems for fractional ordinary differential equations and initial boundary value problems for fractional partial differential equations to prove the well-posedness and other properties.
