Stability and controllability analysis of fractional integro-delay differential equation via delayed perturbation

Abstract

This paper deals with stability and controllability analysis of the system governed by fractional integro delay differential equations. By establishing Finite time stability and Ulam–Hyers stability of fractional integro delay differential equation via delayed perturbation Mittag-Leffler type matrix function. Additionally, we give a suitable Grammian matrix by using a delayed Mittag-Leffler type matrix function. The necessary and sufficient conditions for controllability are established for linear system. Further, by employing Kransnoselskii’s fixed point theorem, the existence of controllability in non-linear case is verified. Finally, an example is provided for better understanding of theoretical aspects.

Keywords

• Fractional integro-delay differential equation
• Delayed Mittag-Leffler type matrix
• Finite time stability
• Ulam–Hyers stability
• Controllability