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A Uniform Method to Ulam–Hyers Stability for Some Linear Fractional Equations

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Abstract

In this paper, we first utilize fractional calculus, the properties of classical and generalized Mittag-Leffler functions to prove the Ulam–Hyers stability of linear fractional differential equations using Laplace transform method. Meanwhile, Ulam–Hyers–Rassias stability result is obtained as a direct corollary. Finally, we apply the same techniques to discuss the Ulam’s type stability of fractional evolution equations, impulsive fractional evolutions equations and Sobolev-type fractional evolution equations.

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Authors and Affiliations

  1. Department of Mathematics, Guizhou University, Guiyang, Guizhou, 550025, People’s Republic of China

    JinRong Wang & Xuezhu Li

Authors
  1. JinRong Wang
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  2. Xuezhu Li
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Correspondence to JinRong Wang.

Additional information

This work is supported by National Natural Science Foundation of China (11201091) and Outstanding Scientific and Technological Innovation Talent Award of Education Department of Guizhou Province ([2014]240).

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Wang, J., Li, X. A Uniform Method to Ulam–Hyers Stability for Some Linear Fractional Equations. Mediterr. J. Math. 13, 625–635 (2016). https://doi.org/10.1007/s00009-015-0523-5

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  • DOI: https://doi.org/10.1007/s00009-015-0523-5

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