Existence and Uniqueness of Solution for a Fractional Riemann-Liouville Initial Value Problem on Time Scales

Abstract

We introduce the concept of fractional derivative of Riemann-Liouville on time scales. Fundamental properties of the new operator are proved, as well as an existence and uniqueness result for a fractional initial value problem on an arbitrary time scale.

This is a preprint of a paper whose final and definite form is in Journal of King Saud University (Science), http://dx.doi.org/10.1016/j.jksus.2015.08.001 Paper submitted 18/May/2015; revised 31/July/2015; accepted for publication 03/Aug/2015

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• Symmetric duality for left and right Riemann-Liouville and Caputo fractional differences
• Time-Fractional Optimal Control of Initial Value Problems on Time Scales
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• Variable order Mittag-Leffler fractional operators on isolated time scales and application to the calculus of variations
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• Right fractional Sobolev space via Riemann$-$Liouville derivatives on time scales and an application to fractional boundary value problem on time scales
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