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Mediterranean Journal of Mathematics

, Volume 13, Issue 2, pp 625–635 | Cite as

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

  • JinRong WangEmail author
  • Xuezhu Li
Article

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.

Keywords

Ulam–Hyers stability Ulam–Hyers–Rassias stability fractional differential equations fractional evolution equations Mittag-Leffler functions 

Mathematics Subject Classification

26A33 34D10 45N05 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of MathematicsGuizhou UniversityGuiyangPeople’s Republic of China

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