Generalized Fractional Operators on Time Scales with Application to Dynamic Equations

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.Comment: This is a preprint whose final and definite form is with 'The European Physical Journal Special Topics' (EPJ ST), ISSN 1951-6355 (Print), ISSN 1951-6401 (Online), available at [https://link.springer.com/journal/11734]. Submitted 20-June-2017; revised 26-Oct-2017; accepted for publication 06-April-2018. arXiv admin note: text overlap with arXiv:1508.00754; text overlap with arXiv:nlin/0507061 by other author