Bounded, asymptotically stable, and L1 solutions of caputo fractional differential equations

• Autorzy: Islam M.N.

Identyfikatory

DOI

http://dx.doi.Org/10.7494/OpMath.2015.35.2.181

• Języki publikacji: EN

Abstrakty

EN

The existence of bounded solutions, asymptotically stable solutions, and L1 solu­tions of a Caputo fractional differential equation has been studied in this paper. The results are obtained from an equivalent Volterra integral equation which is derived by inverting the fractional differential equation. The kernel function of this integral equation is weakly singular and hence the standard techniques that are normally applied on Volterra integral equations do not apply here. This hurdle is overcomed using a resolvent equation and then applying some known properties of the resolvent. In the analysis Schauder's fixed point theorem and Liapunov's method have been employed. The existence of bounded solutions are obtained employing Schauder's theorem, and then it is shown that these solutions are asymptotically stable by a definition found in [C. Avramescu, C. Vladimirescu, On the existence of asymptotically stable solution of certain integral equations, Nonlinear Anal. 66 (2007), 472-483]. Finally, the L1 properties of solutions are obtained using Liapunov's method

Słowa kluczowe

EN

Caputo fractional differential equations; Volterra integral equations; weakly singular kernel; Schauder fixed point theorem; Liapunov's method

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2015
• Tom: Vol. 35, no. 2
• Strony: 181--190
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Islam M.N.

• University of Dayton Department of Mathematics Dayton, OH 45469-2316 USA

Bibliografia

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