Nabla generalized fractional Riemann-Liouville calculus on time scales with an application to dynamic equations

Abstract

We introduce more general concepts of nabla Riemann-Liouville fractional integrals and derivatives ontime scales. Such generalizations on time scales help us to study relations between fractional differenceequations and fractional differential equations. Sufficient conditions for the existence and uniqueness of thesolution to an initial value problem are described by nabla derivatives on time scales. Some properties of thenew operator are proved and illustrated with examples.