We discuss the Laplace transform of the Caputo fractional difference and the fractional discrete Mittag-Leffer functions. On these bases, linear and nonlinear fractional initial value problems are solved by the Laplace transform method.
"Solving Fractional Difference Equations Using the Laplace Transform Method." Abstr. Appl. Anal. 2014 1 - 6, 2014. https://doi.org/10.1155/2014/230850