Abstract
This paper is concerned with fractional abstract Cauchy problems with order α (1,2). The notion of fractional solution operator is introduced, its some properties are obtained. A generation theorem for exponentially bounded fractional solution operators is given. It is proved that the homogeneous fractional Cauchy problem (FACP0) is well-posed if and only if its coefficient operator A generates an α-order fractional solution operator. Sufficient conditions are given to guarantee the existence and uniqueness of mild solutions and strong solutions of the inhomogeneous fractional Cauchy problem (FACPf).
| Original language | English |
|---|---|
| Pages (from-to) | 333-361 |
| Number of pages | 29 |
| Journal | Integral Equations and Operator Theory |
| Volume | 70 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jul 2011 |
Keywords
- Caputo fractional derivative
- fractional abstract Cauchy problem
- fractional solution operator
- Riemann-Liouville fractional derivative
- Riemann-Liouville fractional integral