Ulam–Hyers–Mittag-Leffler stability of fractional-order delay differential equations

Abstract

In this paper, we first prove two existence and uniqueness results for fractional-order delay differential equation with respect to Chebyshev and Bielecki norms. Secondly, we prove the above equation is Ulam–Hyers–Mittag-Leffler stable on a compact interval. Finally, two examples are also provided to illustrate our results.

Keywords:

• Ulam–Hyers–Mittag-Leffler stability
• fractional order
• delay differential equation

AMS Subject Classifications:

• 26A33
• 34D10
• 45N05

Acknowledgements

We acknowledge the valuable comments and suggestions of the anonymous referee and editor Professor Yong Zhou.

Notes

This work is supported by the National Natural Science Foundation of China [11201091], Key Project on the Reforms of Teaching Contents and Course System of Guizhou Normal College and Doctor Project of Guizhou Normal College [13BS010].