International Journal of Difference Equations
We shall consider a linear fractional nabla (backward) fractional difference equation of Riemann–Liouville type with constant coefficients. We apply a transform method to construct solutions. Sufficient conditions in terms of the coefficients are given so that the solutions are absolutely convergent. The method is known for two-term fractional difference equations; the method is new for fractional equations with three or more terms. As a corollary, we exhibit new summation representations of a discrete exponential function, at, t = 0; 1; : : : .
Eloe, Paul W. and Ouyang, Zi, "Multi-term linear fractional nabla difference equations with constant coefficients" (2015). Mathematics Faculty Publications. 111.