Geodesic
Hyers-Ulam stability of fractional linear differential equations involving Caputo fractional derivatives
Applications of Mathematics, Tome 60 (2015) no. 4, pp. 383-393.

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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.
DOI : 10.1007/s10492-015-0102-x
Classification : 26D10, 34A08
Keywords: Hyers-Ulam stability; Laplace transform method; fractional differential equation; Caputo fractional derivative 
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Wang, Chun; Xu, Tian-Zhou. Hyers-Ulam stability of fractional linear differential equations involving Caputo fractional derivatives. Applications of Mathematics, Tome 60 (2015) no. 4, pp. 383-393. doi : 10.1007/s10492-015-0102-x. http://geodesic.mathdoc.fr/articles/10.1007/s10492-015-0102-x/

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