A Lyapunov-type inequality for a fractional boundary value problem
In this work we obtain a Lyapunov-type inequality for a fractional differential equation subject to Dirichlet-type boundary conditions. Moreover, we apply this inequality to deduce a criteria for the nonexistence of real zeros of a certain Mittag-Leffler function.
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| Published in | Fractional calculus & applied analysis Vol. 16; no. 4; pp. 978 - 984 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Vienna
Springer Vienna
01.12.2013
Versita |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1311-0454 1314-2224 |
| DOI | 10.2478/s13540-013-0060-5 |
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| Abstract | In this work we obtain a Lyapunov-type inequality for a fractional differential equation subject to Dirichlet-type boundary conditions. Moreover, we apply this inequality to deduce a criteria for the nonexistence of real zeros of a certain Mittag-Leffler function. |
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| AbstractList | In this work we obtain a Lyapunov-type inequality for a fractional differential equation subject to Dirichlet-type boundary conditions. Moreover, we apply this inequality to deduce a criteria for the nonexistence of real zeros of a certain Mittag-Leffler function. |
| Author | Ferreira, Rui A. C. |
| Author_xml | – sequence: 1 givenname: Rui A. C. surname: Ferreira fullname: Ferreira, Rui A. C. email: ruiacferreira@ulusofona.pt organization: Department of Mathematics, Lusophone University of Humanities and Technologies, Center for Research and Development in Mathematics and Applications |
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| Cites_doi | 10.1016/j.jmaa.2005.02.052 10.1016/S0304-0208(06)80001-0 10.1007/978-94-011-4339-4_1 |
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| Keywords | Secondary: 26D10, 34C10, 33E12 Lyapunov’s inequality Mittag-Leffler function Primary: 34A08, 34A40 fractional derivative, Green’s function |
| Language | English |
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| References | Tiryaki (CR8) 2010; 5 Lyapunov (CR4) 1907; 2 Rahimy (CR7) 2010; 4 Bai, Lü (CR1) 2005; 311 Popov (CR6) 2006; 12 Brown, Hinton, Rassias (CR2) 2000 Nahušev (CR5) 1977; 234 Kilbas, Srivastava, Trujillo (CR3) 2006 A M Lyapunov (60_CR4) 1907; 2 AM Nahušev (60_CR5) 1977; 234 AYu Popov (60_CR6) 2006; 12 M Rahimy (60_CR7) 2010; 4 RC Brown (60_CR2) 2000 AA Kilbas (60_CR3) 2006 Z Bai (60_CR1) 2005; 311 A Tiryaki (60_CR8) 2010; 5 |
| References_xml | – volume: 234 start-page: 308 issue: 2 year: 1977 end-page: 311 ident: CR5 article-title: The Sturm-Liouville problem for a second order ordinary differential equation with fractional derivatives in the lower terms publication-title: Dokl. Akad. Nauk SSSR – volume: 2 start-page: 27 year: 1907 end-page: 247 ident: CR4 article-title: Probleme général de la stabilité du mouvement, (French Transl. of a Russian paper dated 1893) publication-title: Ann. Fac. Sci. Univ. Toulouse – volume: 4 start-page: 2453 issue: 49–52 year: 2010 end-page: 2461 ident: CR7 article-title: Applications of fractional differential equations publication-title: Appl. Math. Sci – volume: 12 start-page: 137 issue: 6 year: 2006 end-page: 155 ident: CR6 article-title: On the number of real eigenvalues of a certain boundaryvalue problem for a second-order equation with fractional derivative publication-title: Fundam. Prikl. Mat. – volume: 5 start-page: 231 issue: 2 year: 2010 end-page: 248 ident: CR8 article-title: Recent developments of Lyapunov-type inequalities publication-title: Adv. Dyn. Syst. Appl. – volume: 311 start-page: 495 issue: 2 year: 2005 end-page: 505 ident: CR1 article-title: Positive solutions for boundary value problem of nonlinear fractional differential equation publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2005.02.052 – year: 2006 ident: CR3 publication-title: Theory and Applications of Fractional Differential Equations doi: 10.1016/S0304-0208(06)80001-0 – start-page: 1 year: 2000 end-page: 25 ident: CR2 article-title: Lyapunov inequalities and their applications publication-title: Survey on Classical Inequalities doi: 10.1007/978-94-011-4339-4_1 – volume: 234 start-page: 308 issue: 2 year: 1977 ident: 60_CR5 publication-title: Dokl. Akad. Nauk SSSR – volume: 12 start-page: 137 issue: 6 year: 2006 ident: 60_CR6 publication-title: Fundam. Prikl. Mat. – volume: 2 start-page: 27 year: 1907 ident: 60_CR4 publication-title: Ann. Fac. Sci. Univ. Toulouse – start-page: 1 volume-title: Survey on Classical Inequalities year: 2000 ident: 60_CR2 doi: 10.1007/978-94-011-4339-4_1 – volume: 311 start-page: 495 issue: 2 year: 2005 ident: 60_CR1 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2005.02.052 – volume: 4 start-page: 2453 issue: 49–52 year: 2010 ident: 60_CR7 publication-title: Appl. Math. Sci – volume: 5 start-page: 231 issue: 2 year: 2010 ident: 60_CR8 publication-title: Adv. Dyn. Syst. Appl. – volume-title: Theory and Applications of Fractional Differential Equations year: 2006 ident: 60_CR3 doi: 10.1016/S0304-0208(06)80001-0 |
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| Snippet | In this work we obtain a Lyapunov-type inequality for a fractional differential equation subject to Dirichlet-type boundary conditions. Moreover, we apply this... |
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| SubjectTerms | Abstract Harmonic Analysis Analysis fractional derivative, Green’s function Functional Analysis Integral Transforms Lyapunov’s inequality Mathematics Mathematics and Statistics Mittag-Leffler function Operational Calculus Primary: 34A08, 34A40 Research Paper Secondary: 26D10, 34C10, 33E12 |
| Title | A Lyapunov-type inequality for a fractional boundary value problem |
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