Nabla generalized fractional Riemann-Liouville calculus on time scales with an application to dynamic equations
Keywords:Time scales, fractional derivatives, dynamic equations, initial value problems 2010 MSC: 26A33, 34K37, 34N05.
We introduce more general concepts of nabla Riemann-Liouville fractional integrals and derivatives on
time scales. Such generalizations on time scales help us to study relations between fractional difference
equations and fractional differential equations. Sufficient conditions for the existence and uniqueness of the
solution to an initial value problem are described by nabla derivatives on time scales. Some properties of the
new operator are proved and illustrated with examples.
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