Cauchy's formula on nonempty closed sets and a new notion of Riemann--Liouville fractional integral on time scales

Abstract

We prove Cauchy's formula for repeated integration on time scales. The obtained relation gives rise to new notions of fractional integration and differentiation on arbitrary nonempty closed sets.

This is a preprint of a paper whose final and definite form is published by 'Applied Mathematics Letters' (ISSN: 0893-9659), available at [https://doi.org/10.1016/j.aml.2021.107407]. Please cite this article as: D.F.M. Torres, Cauchy's formula on nonempty closed sets and a new notion of Riemann-Liouville fractional integral on time scales, Appl. Math. Lett. 121 (2021), Art. 107407, 6 pp

References in corpus (3)

• Discrete-Time Fractional Variational Problems
• Necessary Optimality Conditions for Fractional Difference Problems of the Calculus of Variations
• Fractional Derivatives and Integrals on Time Scales via the Inverse Generalized Laplace Transform

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