A Conformable Fractional Calculus on Arbitrary Time Scales

Nadia Benkhettou; Salima Hassani; Delfim F. M. Torres

doi:10.1016/j.jksus.2015.05.003

A Conformable Fractional Calculus on Arbitrary Time Scales

Classical Analysis and ODEs 2015-12-24 v1

Authors: Nadia Benkhettou , Salima Hassani , Delfim F. M. Torres

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Abstract

A conformable time-scale fractional calculus of order $\alpha \in ]0,1]$ is introduced. The basic tools for fractional differentiation and fractional integration are then developed. The Hilger time-scale calculus is obtained as a particular case, by choosing $\alpha = 1$ .

Keywords

fractional calculus fractional differential equations differential equations

Cite

@article{arxiv.1505.03134,
  title  = {A Conformable Fractional Calculus on Arbitrary Time Scales},
  author = {Nadia Benkhettou and Salima Hassani and Delfim F. M. Torres},
  journal= {arXiv preprint arXiv:1505.03134},
  year   = {2015}
}

Comments

This is a preprint of a paper whose final and definite form is in Journal of King Saud University (Science), ISSN 1018-3647. Paper submitted 14/April/2015; revised 12/May/2015; accepted for publication 12/May/2015. arXiv admin note: text overlap with arXiv:1405.2813

A Conformable Fractional Calculus on Arbitrary Time Scales

Abstract

Keywords

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