On the stabilization of a coupled fractional ordinary and partial differential equations†

Document Type : Research Article

Authors

• S. Amiri ¹
• M. Keyanpour ²

¹ Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.

² Faculty of Mathematical Sciences, and Center of Excellence for Mathematical Modelling, Optimization and Combinational Computing (MMOCC), University of Guilan, Rasht, Iran.

10.22067/ijnao.v10i1.84902

Abstract

We investigate the stabilization problem of a cascade of a fractional ordinary differential equation (FODE) and a fractional diffusion (FD) equation, where the interconnections are of Neumann type. We exploit the PDE back stepping method as a powerful tool for designing a controller to show the Mittag–Leffler stability of the FD-FODE cascade. Finally, numerical simulations are presented to verify the results.

Keywords

• Backstepping
• Stability
• Fractional-order cascaded systems

20.1001.1.24236977.2020.10.1.11.1

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