Abstract:

We studied the existence and uniqueness of solutions for a class of the sequential fractional q-differences equation. Firstly, a representation for the solution to this equation was given via q-exponential. Then the existence and uniqueness of solutions were proven by means of Banach fixed point theorem, Krasnoselskii fixed point theorem and LeraySchauder alternative theorem.

Key words: sequential fractional q-difference, fixed point theorem, existence of solutions