Fractional Differential Equations in Terms of Comparison Results and Lyapunov Stability with Initial Time Difference
The qualitative behavior of a perturbed fractional-order differential equation with Caputo's derivative that differs in initial position and initial time with respect to the unperturbed fractional-order differential equation with Caputo's derivative has been investigated. We compare the cl...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/762857 |
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| _version_ | 1832545620018069504 |
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| author | Coşkun Yakar |
| author_facet | Coşkun Yakar |
| author_sort | Coşkun Yakar |
| collection | DOAJ |
| description | The qualitative behavior of a perturbed fractional-order differential equation with Caputo's derivative that differs in initial position and initial time with respect to the unperturbed fractional-order differential equation with Caputo's derivative has been investigated. We compare the classical notion of stability to the notion of initial time difference stability for fractional-order differential equations in Caputo's sense. We present a comparison result which again gives the null solution a central role in the comparison fractional-order differential equation when establishing initial time difference stability of the perturbed fractional-order differential equation with respect to the unperturbed fractional-order differential equation. |
| format | Article |
| id | doaj-art-03195f20d3204113bd7467efd900017a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-03195f20d3204113bd7467efd900017a2025-02-03T07:25:12ZengWileyAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/762857762857Fractional Differential Equations in Terms of Comparison Results and Lyapunov Stability with Initial Time DifferenceCoşkun Yakar0Department of Mathematics, Gebze Institute of Technology, Gebze-Kocaeli 141-41400, TurkeyThe qualitative behavior of a perturbed fractional-order differential equation with Caputo's derivative that differs in initial position and initial time with respect to the unperturbed fractional-order differential equation with Caputo's derivative has been investigated. We compare the classical notion of stability to the notion of initial time difference stability for fractional-order differential equations in Caputo's sense. We present a comparison result which again gives the null solution a central role in the comparison fractional-order differential equation when establishing initial time difference stability of the perturbed fractional-order differential equation with respect to the unperturbed fractional-order differential equation.http://dx.doi.org/10.1155/2010/762857 |
| spellingShingle | Coşkun Yakar Fractional Differential Equations in Terms of Comparison Results and Lyapunov Stability with Initial Time Difference Abstract and Applied Analysis |
| title | Fractional Differential Equations in Terms of Comparison Results and Lyapunov Stability with Initial Time Difference |
| title_full | Fractional Differential Equations in Terms of Comparison Results and Lyapunov Stability with Initial Time Difference |
| title_fullStr | Fractional Differential Equations in Terms of Comparison Results and Lyapunov Stability with Initial Time Difference |
| title_full_unstemmed | Fractional Differential Equations in Terms of Comparison Results and Lyapunov Stability with Initial Time Difference |
| title_short | Fractional Differential Equations in Terms of Comparison Results and Lyapunov Stability with Initial Time Difference |
| title_sort | fractional differential equations in terms of comparison results and lyapunov stability with initial time difference |
| url | http://dx.doi.org/10.1155/2010/762857 |
| work_keys_str_mv | AT coskunyakar fractionaldifferentialequationsintermsofcomparisonresultsandlyapunovstabilitywithinitialtimedifference |