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Geometric Interpretation of Fractional-Order Derivative

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Abstract

A new geometric interpretation of the Riemann-Liouville and Caputo derivatives of non-integer orders is proposed. The suggested geometric interpretation of the fractional derivatives is based on modern differential geometry and the geometry of jet bundles. We formulate a geometric interpretation of the fractional-order derivatives by using the concept of the infinite jets of functions. For this interpretation, we use a representation of the fractional-order derivatives by infinite series with integer-order derivatives. We demonstrate that the derivatives of non-integer orders connected with infinite jets of special type. The suggested infinite jets are considered as a reconstruction from standard jets with respect to order.

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  1. Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, 119991, Russia

    Vasily E. Tarasov

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Tarasov, V.E. Geometric Interpretation of Fractional-Order Derivative. FCAA 19, 1200–1221 (2016). https://doi.org/10.1515/fca-2016-0062

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