Chain rules and inequalities for the BHT fractional calculus on arbitrary time scales

Abstract

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

arXiv commentThis is a preprint of a paper whose final and definite form is published in 'Arabian Journal of Mathematics', ISSN 2193-5343 (Print) 2193-5351 (Online). Paper submitted 25/Feb/2016; revised 24/Sept/2016; accepted 28/Nov/2016

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Cited by in corpus (7)

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• Novel results on Hermite-Hadamard kind inequalities for $\eta$-convex functions by means of $(k,r)$-fractional integral operators
• Analysis of fractional integro-differential equations of thermistor type
• A Truly Conformable Calculus on Time Scales