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Hyers-Ulam stability of fractional linear differential equations involving Caputo fractional derivatives

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Abstract

The aim of this paper is to study the stability of fractional differential equations in Hyers-Ulam sense. Namely, if we replace a given fractional differential equation by a fractional differential inequality, we ask when the solutions of the fractional differential inequality are close to the solutions of the strict differential equation. In this paper, we investigate the Hyers-Ulam stability of two types of fractional linear differential equations with Caputo fractional derivatives. We prove that the two types of fractional linear differential equations are Hyers-Ulam stable by applying the Laplace transform method. Finally, an example is given to illustrate the theoretical results.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, P.R. China

    Chun Wang & Tian-Zhou Xu

  2. Department of Mathematics, Changzhi University, Changzhi, Shanxi, 046011, P.R. China

    Chun Wang

Authors
  1. Chun Wang
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  2. Tian-Zhou Xu
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Corresponding author

Correspondence to Chun Wang.

Additional information

This work is supported by the National Natural Science Foundation of China (11171022).

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Wang, C., Xu, TZ. Hyers-Ulam stability of fractional linear differential equations involving Caputo fractional derivatives. Appl Math 60, 383–393 (2015). https://doi.org/10.1007/s10492-015-0102-x

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  • DOI: https://doi.org/10.1007/s10492-015-0102-x

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