论文标题
针对Caputo和Riemann-Liouville衍生品的分数类似Stefan的问题的明确解决方案
Explicit Solutions to Fractional Stefan-like problems for Caputo and Riemann-Liouville Derivatives
论文作者
论文摘要
通过使用riemann-liouville和caputo衍生品$α\ in（0，1）$验证它们是否在$α= 1 $时在极限情况下与相同的经典stefan问题相吻合，考虑了两个分数两相的问题。对于这两个问题，就介绍了赖特功能的明确解决方案。即使这两个解决方案的相似性，也提供了证明它们与众不同的证明。当$α\附近1 $的$α\时，将收敛到同一经典解决方案的其他解决方案。还提供和分析了问题的无量纲版本的数值示例。
Two fractional two-phase Stefan-like problems are considered by using Riemann-Liouville and Caputo derivatives of order $α\in (0, 1)$ verifying that they coincide with the same classical Stefan problem at the limit case when $α=1$. For both problems, explicit solutions in terms of the Wright functions are presented. Even though the similarity of the two solutions, a proof that they are different is also given. The convergence when $α\nearrow 1$ of the one and the other solutions to the same classical solution is given. Numerical examples for the dimensionless version of the problem are also presented and analyzed.
