论文标题
分数微分方程的初始，内部和内边界问题
Initial, inner and inner-boundary problems for a fractional differential equation
论文作者
论文摘要
众所周知，人们可以考虑使用Caputo衍生物的演化方程式的库奇问题，但对Riemann-Liouville衍生品的初始价值问题的情况却较少了解。在本文中，我们提出了带有Riemann-Liouville衍生物的分数微分方程的新型初始，内部和内部边界值问题。证明了有关存在和独特性的结果，并发现了解决性的条件。还讨论了新型初始，内部和内部条件的适当性。此外，我们为解决方案提供明确的公式。作为一般阳性运算符的应用分数部分微分方程。
While it is known that one can consider the Cauchy problem for evolution equations with Caputo derivatives, the situation for the initial value problems for the Riemann-Liouville derivatives is less understood. In this paper we propose new type initial, inner and inner-boundary value problems for fractional differential equations with the Riemann-Liouville derivatives. The results on the existence and uniqueness are proved, and conditions on the solvability are found. The well-posedness of the new type initial, inner and inner-boundary conditions are also discussed. Moreover, we give explicit formulas for the solutions. As an application fractional partial differential equations for general positive operators are studied.
