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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The authors thank the referees for their careful reading of the manuscript and insightful comments, which helped to improve the quality of the paper. We would also like to acknowledge the valuable comments and suggestions from the editors, which vastly contributed to improve the presentation of the paper.
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This work is supported by the National Natural Science Foundation of China (11201091), Key Projects of Science and Technology Research in the Chinese Ministry of Education (211169), Key Support Subject (Applied Mathematics) and Key project on the reforms of teaching contents and course system of Guizhou Normal College.
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Wang, J., Li, X. E α -Ulam type stability of fractional order ordinary differential equations. J. Appl. Math. Comput. 45, 449–459 (2014). https://doi.org/10.1007/s12190-013-0731-8
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DOI: https://doi.org/10.1007/s12190-013-0731-8