Formalization of Fractional Flow Component in Higher-Order Logic Theorem Proving

Abstract

Fractional calculus is a powerful tool for dealing with complex systems, and fractional flow component can effectively reflect the nonlinear gradual change of rheology in vibration state. Besides, higher-order logic theorem proving is a formal method for specification and verification. This paper, accordingly, presents a higher-order logic formalization of fractional flow component based on fractional calculus Caputo definition. The relationship between fractional order differential and integer order differential is verified according to fractional calculus Caputo definition in higher-order logic theorem proving, where fluid mechanics fractional flow component is then formally analyzed.