Solvability and stability of multi-term fractional delay \(q\)-difference equation. (English) Zbl 07923999
Summary: 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 multi-term 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.
MSC:
| 39A13 | Difference equations, scaling (\(q\)-differences) |
| 39A27 | Boundary value problems for difference equations |
| 39A30 | Stability theory for difference equations |
| 39A70 | Difference operators |
| 26A33 | Fractional derivatives and integrals |
Keywords:
fractional \(q\)-difference equations; boundary value problems; multi-term operators; existence and uniqueness; functional stabilityReferences:
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