Stability of the nonlinear fractional differential equations with the right-sided Riemann-Liouville fractional derivative

Chun Wang; Tian-Zhou Xu

doi:10.3934/dcdss.2017025

Article Contents

2017, Volume 10, Issue 3: 505-521. Doi: 10.3934/dcdss.2017025

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Stability of the nonlinear fractional differential equations with the right-sided Riemann-Liouville fractional derivative

Chun Wang^1,2, , and
Tian-Zhou Xu^1,

1.
School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China
2.
Department of Mathematics, Changzhi University, Changzhi Shanxi 046011, China

^* Corresponding author
^* Corresponding author

Received: May 31, 2016

Revised: December 31, 2016

Published: May 2017

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Abstract

In this paper, using the weighted space method and a fixed point theorem, we investigate the Hyers-Ulam-Rassias stability of the nonlinear fractional differential equations with the right-sided Riemann-Liouville derivative on the continuous function space. We obtain some sufficient conditions in order that the nonlinear fractional differential equations are stable on the continuous function space. The results improve and extend some recent results. Finally, we construct some examples to illustrate the theoretical results.

Keywords:

Hyers-Ulam-Rassias stability,
Hyers-Ulam stability,
nonlinear fractional differential equation,
weighted space method,
fixed point method,
continuous function space.

Mathematics Subject Classification: Primary: 47H10; Secondary: 47J05.

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References

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