Ulam-type stability for a class of implicit fractional differential equations with non-instantaneous integral impulses and boundary condition. (English) Zbl 1444.34083
Summary: In this paper, we investigate four different types of Ulam stability, i.e., Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for a class of nonlinear implicit fractional differential equations with non-instantaneous integral impulses and nonlinear integral boundary condition. We also establish certain conditions for the existence and uniqueness of solutions for such a class of fractional differential equations using Caputo fractional derivative. The arguments are based on generalized Diaz-Margolis’s fixed point theorem. We provide two examples, which shows the validity of our main results.
MSC:
| 34K20 | Stability theory of functional-differential equations |
| 26A33 | Fractional derivatives and integrals |
| 34A08 | Fractional ordinary differential equations |
Keywords:
Caputo fractional derivative; implicit fractional differential equations; fractional integral; non-instantaneous impulses; Ulam-type stability; Diaz-Margolis’s fixed point theoremReferences:
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