Abstract
In this paper, the concepts of \(\mathbb{E}_{\alpha}\)-Ulam-Hyers stability, generalized \(\mathbb{E}_{\alpha}\)-Ulam-Hyers stability, \(\mathbb{E}_{\alpha}\)-Ulam-Hyers-Rassias stability and generalized \(\mathbb{E}_{\alpha}\)-Ulam-Hyers-Rassias stability for fractional order ordinary differential equations are raised. Without loss of generality, \(\mathbb{E}_{\alpha}\)-Ulam-Hyers-Rassias stability result is derived by using a singular integral inequality of Gronwall type. Two examples are also provided to illustrate our results.
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