Well-posedness of equations with fractional derivative via the method of sum

作者：Bu Shang Quan^*

来源：Acta Mathematica Sinica-English Series, 2012, 28(1): 37-44.

DOI：10.1007/s10114-012-0333-7

• Well-posedness
• fractional derivative
• the method of sum
• real interpolation spaces
• fractional Sobolev spaces

We study the well-posedness of the equations with fractional derivative D (alpha) u(t) = Au(t)+ f(t) (0 a parts per thousand currency sign t a parts per thousand currency sign 2 pi), where A is a closed operator in a Banach space X, 0 < alpha < 1 and D (alpha) is the fractional derivative in the sense of Weyl. Although this problem is not always well-posed in L (p) (0, 2 pi;X) or periodic continuous function spaces C (per)([0, 2 pi];X), we show by using the method of sum that it is well-posed in some subspaces of L (p) (0, 2 pi;X) or C (per)([0, 2 pi];X).

• 出版日期2012-1
• 单位清华大学