| Variation of Constant Formulae for Time Invariant and Time Varying Caputo Fractional Delay Differential Systems |
| Received:October 22, 2013 Revised:March 20, 2014 |
| Key Words:
fractional delay differential systems variation formula exponential estimates Laplace transform Gronwall's integral inequality.
|
| Fund Project:Supported by the Programs of Educational Commission of Anhui Province (Grant Nos.KJ2011A197;KJ2013Z186). |
|
| Hits: 3033 |
| Download times: 3641 |
| Abstract: |
| This paper studies the variation of constant formulae for linear Caputo fractional delay differential systems. We discuss the exponential estimates of the solutions for linear time invariant fractional delay differential systems by using the Gronwall's integral inequality. The variation of constant formula for linear time invariant fractional delay differential systems is obtained by using the Laplace transform method. In terms of the superposition principle of linear systems and fundamental solution matrix, we also establish the variation of constant formula for linear time varying fractional delay differential systems. The obtained results generalize the corresponding ones of integer-order delayed differential equations. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2014.05.006 |
| View Full Text View/Add Comment |
