Chain rules and inequalities for the BHT fractional calculus on arbitrary timescales

Abstract

We develop the Benkhettou–Hassani–Torres fractional (noninteger order) calculus on timescales by proving two chain rules for the α-fractional derivative and five inequalities for the α-fractional integral. The results coincide with well-known classical results when the operators are of (integer) order α = 1 and the timescale coincides with the set of real numbers.