Boundary control of a fractional reaction-diffusion equation coupled with fractional ordinary differential equations with delay

Mimi Hou, Xuan-Xuan Xi and Xian-Feng Zhou

Applied Mathematics and Computation, 2021, vol. 406, issue C

Abstract: This paper deals with boundary feedback control for a fractional reaction-diffusion equation with varying coefficient coupled with fractional ordinary differential equations with delay, which is a generalization of integer order coupled system. By designing a state feedback controller, we transform an unstable system into an asymptotic stable system via the backstepping method. The exact solution of the target system is given by the Prabhakar function. We also obtain the exact solution of the original system with the help of the invertible coordinate transformation. Furthermore, by the fractional Halanay’s inequality, we structure a Lyapunov functional to prove the asymptotic stability of the given system. Finally, a numerical simulation example is provided to illustrate the applications of our results.

Keywords: Asymptotic stability; Fractional derivative; Lyapunov functional; Coupled system; Boundary feedback control (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:406:y:2021:i:c:s0096300321003490

DOI: 10.1016/j.amc.2021.126260

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