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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.
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

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