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

Chun Wang; Tian-Zhou Xu

Applications of Mathematics (2015)

  • Volume: 60, Issue: 4, page 383-393
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Wang, Chun, and Xu, Tian-Zhou. "Hyers-Ulam stability of fractional linear differential equations involving Caputo fractional derivatives." Applications of Mathematics 60.4 (2015): 383-393. <http://eudml.org/doc/271626>.

@article{Wang2015,
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.},
author = {Wang, Chun, Xu, Tian-Zhou},
journal = {Applications of Mathematics},
keywords = {Hyers-Ulam stability; Laplace transform method; fractional differential equation; Caputo fractional derivative; Hyers-Ulam stability; Laplace transform method; fractional differential equation; Caputo fractional derivative},
language = {eng},
number = {4},
pages = {383-393},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Hyers-Ulam stability of fractional linear differential equations involving Caputo fractional derivatives},
url = {http://eudml.org/doc/271626},
volume = {60},
year = {2015},
}

TY - JOUR
AU - Wang, Chun
AU - Xu, Tian-Zhou
TI - Hyers-Ulam stability of fractional linear differential equations involving Caputo fractional derivatives
JO - Applications of Mathematics
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 4
SP - 383
EP - 393
AB - 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.
LA - eng
KW - Hyers-Ulam stability; Laplace transform method; fractional differential equation; Caputo fractional derivative; Hyers-Ulam stability; Laplace transform method; fractional differential equation; Caputo fractional derivative
UR - http://eudml.org/doc/271626
ER -

References

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