Existence and Hyers-Ulam stability results for a class of fractional order delay differential equations with non-instantaneous impulses. (English) Zbl 1490.74036
Summary: In this paper, we mainly consider the existence and Hyers-Ulam stability of solutions for a class of fractional differential equations involving time-varying delays and non-instantaneous impulses. By the Krasnoselskii’s fixed point theorem, we present the new constructive existence results for the addressed equation. In addition, we deduce that the equations have Hyers-Ulam stable solutions by utilizing generalized Grönwall’s inequality. Some results in this literature are new and improve some early conclusions.
MSC:
| 74H20 | Existence of solutions of dynamical problems in solid mechanics |
| 34D20 | Stability of solutions to ordinary differential equations |
| 26A33 | Fractional derivatives and integrals |
Keywords:
fractional differential equation; existence; Hyers-Ulam stability; time-varying delays; non-instantaneous impulsesReferences:
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