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Fractional calculus on time scales with Taylor’s theorem

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Abstract

We present a definition of the Riemann-Liouville fractional calculus for arbitrary time scales through the use of time scales power functions, unifying a number of theories including continuum, discrete and fractional calculus. Basic properties of the theory are introduced including integrability conditions and index laws. Special emphasis is given to extending Taylor’s theorem to incorporate our theory.

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  1. Department of Mathematics and Statistics, University of Melbourne, VIC, 3010, Australia

    Paul Anthony Williams

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  1. Paul Anthony Williams
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Williams, P.A. Fractional calculus on time scales with Taylor’s theorem. fcaa 15, 616–638 (2012). https://doi.org/10.2478/s13540-012-0043-y

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  • DOI: https://doi.org/10.2478/s13540-012-0043-y

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