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Generalized fractional operators on time scales with application to dynamic equations

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Abstract

We introduce more general concepts of Riemann–Liouville fractional integral and derivative on time scales, of a function with respect to another function. Sufficient conditions for existence and uniqueness of solution to an initial value problem described by generalized fractional order differential equations on time scales are proved.

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Authors and Affiliations

  1. Institute of Sciences, Department of Mathematics, University of Ain Temouchent, BP 284, 46000, Ain Temouchent, Algeria

    Kheira Mekhalfi

  2. Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193, Aveiro, Portugal

    Delfim F. M. Torres

Authors
  1. Kheira Mekhalfi
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  2. Delfim F. M. Torres
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Correspondence to Delfim F. M. Torres.

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Mekhalfi, K., Torres, D.F.M. Generalized fractional operators on time scales with application to dynamic equations. Eur. Phys. J. Spec. Top. 226, 3489–3499 (2017). https://doi.org/10.1140/epjst/e2018-00036-0

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  • DOI: https://doi.org/10.1140/epjst/e2018-00036-0

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