A practical formula of solutions for a family of linear non-autonomous fractional nabla difference equations

In this article, we focus on a generalized problem of linear non-autonomous fractional nabla difference equations. Firstly, we define the equations and describe how this family of problems covers other linear fractional difference equations that appear in the literature. Then, by using matrix theory we provide a new practical formula of solutions for these type of equations. Finally, numerical examples are given to justify our theory.