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A survey on the stability of fractional differential equations

Dedicated to Prof. Y.S. Chen on the Occasion of his 80th Birthday

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Abstract.

Recently, fractional calculus has attracted much attention since it plays an important role in many fields of science and engineering. Especially, the study on stability of fractional differential equations appears to be very important. In this paper, a brief overview on the recent stability results of fractional differential equations and the analytical methods used are provided. These equations include linear fractional differential equations, nonlinear fractional differential equations, fractional differential equations with time-delay. Some conclusions for stability are similar to that of classical integer-order differential equations. However, not all of the stability conditions are parallel to the corresponding classical integer-order differential equations because of non-locality and weak singularities of fractional calculus. Some results and remarks are also included.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, PR China

    C.P. Li & F.R. Zhang

  2. School of Mathematics and Computational Sciences, China University of Petroleum (East China), Dongying, 257061, PR China

    F.R. Zhang

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  1. C.P. Li
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  2. F.R. Zhang
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Correspondence to C.P. Li or F.R. Zhang.

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Li, C., Zhang, F. A survey on the stability of fractional differential equations. Eur. Phys. J. Spec. Top. 193, 27–47 (2011). https://doi.org/10.1140/epjst/e2011-01379-1

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