Abstract
We give necessary and suflicient conditions for an unbounded closed operator A in a Banach space X such that the abstract Cauchy problem for the fractional evolution equation Dau = Au, 0 <a <1, can be solved. We also present conditions on A such that the fractional time evolution is holomorphic. Arelation between the solutions of the problem for different a, 0 < a = 1, is obtained. In particular, this relation shows that the problem has a holomorphic solution whenever A generates just a Co-semigroup.
Some examples are given.
| Original language | English |
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| Pages (from-to) | 255-270 |
| Journal | Fractional Calculus and Applied Analysis |
| Volume | 1 |
| Issue number | 3 |
| Publication status | Published - 1998 |