Integral Solutions of an Initial Value Problem of Fractional Dynamic Equations on Time Scale

The purpose of this paper is to investigate the existence of the integral solution of a fractional dynamic problem in the domain of time scale calculus. The discussion has been done with the help of Schauder’s fixed point theorem and the Kolmogorov compactness criterion in time scales. The new notion of the Caputo derivative in terms of nabla derivative (Caputo Formula: see text-derivative) is developed with the help of the recently developed new notion of Riemann–Liouville nabla derivative (Riemann–Liouville Formula: see text-derivative). Some properties of the Caputo Formula: see text-derivative are also discussed. Later, examples have been given to justify the main findings of the paper.