Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
Model checking
Fractional differentiation for edge detection
Signal Processing - Special issue: Fractional signal processing and applications
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
Functional Fractional Calculus for System Identification and Controls
Functional Fractional Calculus for System Identification and Controls
Fractional order control: a tutorial
ACC'09 Proceedings of the 2009 conference on American Control Conference
Formal analysis of fractional order systems in HOL
Proceedings of the International Conference on Formal Methods in Computer-Aided Design
On the formalization of the lebesgue integration theory in HOL
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Formal analysis of fractional order systems in HOL
Proceedings of the International Conference on Formal Methods in Computer-Aided Design
Formal probabilistic analysis of cyber-physical transportation systems
ICCSA'12 Proceedings of the 12th international conference on Computational Science and Its Applications - Volume Part III
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Fractional order systems, which involve integration and differentiation of non integer order, are increasingly being used in the fields of control systems, robotics, signal processing and circuit theory. Traditionally, the analysis of fractional order systems has been performed using paper-and-pencil based proofs or computer algebra systems. These analysis techniques compromise the accuracy of their results and thus are not recommended to be used for safety-critical fractional order systems. To overcome this limitation, we propose to leverage upon the high expressiveness of higher-order logic to formalize the theory of fractional calculus, which is the foremost mathematical concept in analyzing fractional order systems. This paper provides a higher-order-logic formalization of fractional calculus based on the Riemann-Liouville approach using the HOL theorem prover. To demonstrate the usefulness of the reported formalization, we utilize it to formally analyze some fractional order systems, namely, a fractional electrical component Resistoductance, a fractional integrator and a fractional differentiator circuit.