Abstract
This paper presents a formalization of a fractional order linear system in a higher-order logic (HOL) theorem proving system. Based on the formalization of the Grünwald–Letnikov (GL) definition, we formally specify and verify the linear and superposition properties of fractional order systems. The proof provides a rigor and solid underpinnings for verifying concrete fractional order linear control systems. Our implementation in HOL demonstrates the effectiveness of our approach in practical applications.
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