Eur. Phys. J. Special Topics 226, 3489–3499 (2017)
https://doi.org/10.1140/epjst/e2018-00036-0

Regular Article

Generalized fractional operators on time scales with application to dynamic equations

¹ Institute of Sciences, Department of Mathematics, University of Ain Temouchent, BP 284, 46000 Ain Temouchent, Algeria
² Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

^a e-mail: delfim@ua.pt

Received: 20 June 2017
Received in final form: 26 October 2017
Published online: 25 July 2018

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.