SOLVABILITY AND STABILITY OF MULTI-TERM FRACTIONAL DELAY Q-DIFFERENCE EQUATION

The research of multi -term fractional differential equations has attracted the attention of scholars and obtained abundant results in recent years. However, there are few studies on the multi -term fractional q-difference equations. In this paper, we investigate boundary value problems for multiterm fractional delay q-difference equation. By virtue of Banach contraction mapping principle and Leray-Schauder nonlinear alternative theorem, we obtain the uniqueness and existence of the solution. In addition, we get four different results for functional stability, including Ulam-Hyres stability, generalized Ulam-Hyres stability, Ulam-Hyres Rassias stability and generalized Ulam-Hyres Rassias stability. Finally, give relevant examples to demonstrate the main results.