Infinite series representation of fractional calculus: theory and applications

Yiheng Wei; YangQuan Chen; Qing Gao; Yong Wang

doi:10.1109/cac48633.2019.8997499

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arXiv · 1901.11134

Infinite series representation of fractional calculus: theory and applications

Yiheng Wei·YangQuan Chen·Qing Gao·Yong Wang

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Abstract

This paper focuses on the equivalent expression of fractional integrals/derivatives with an infinite series. A universal framework for fractional Taylor series is developed by expanding an analytic function at the initial instant or the current time. The framework takes into account of the Riemann-Liouville definition, the Caputo definition, the constant order and the variable order. On this basis, some properties of fractional calculus are confirmed conveniently. An intuitive numerical approximation scheme via truncation is proposed subsequently. Finally, several illustrative examples are presented to validate the effectiveness and practicability of the obtained results.

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BibTeX RIS

Yiheng Wei, YangQuan Chen, Qing Gao, Yong Wang. 2019-01-26. Infinite series representation of fractional calculus: theory and applications. https://doi.org/10.1109/cac48633.2019.8997499

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