Abstract
In this work, by constructing fundamental solutions and using the theory of resolvent operators and fractional powers of operators, we study the approximate controllability of a class of semi-linear stochastic integro-differential equations with infinite delay in Lp space (2 < p < ∞). Sufficient conditions for approximate controllability of the discussed equations are obtained under the assumption that the associated deterministic linear system is approximately controllable. An example is provided to illustrate the obtained results.
| Original language | English |
|---|---|
| Pages (from-to) | 1133-1167 |
| Number of pages | 35 |
| Journal | IMA Journal of Mathematical Control and Information |
| Volume | 37 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2020 |
Keywords
- Approximate controllability
- Fundamental solution
- Infinite delay
- Resolvent operator
- Stochastic integro-differential equation