Fractional boundary value problems and Lyapunov-type inequalities with fractional integral boundary conditions
We discuss boundary value problems for Riemann-Liouville fractional differential equations with certain fractional integral boundary conditions. Such boundary conditions are different from the widely considered pointwise conditions in the sense that they allow solutions to have singularities, and di...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2016-06-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4879 |
| _version_ | 1797830617936691200 |
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| author | Sougata Dhar Qingkai Kong Michael McCabe |
| author_facet | Sougata Dhar Qingkai Kong Michael McCabe |
| author_sort | Sougata Dhar |
| collection | DOAJ |
| description | We discuss boundary value problems for Riemann-Liouville fractional differential equations with certain fractional integral boundary conditions. Such boundary conditions are different from the widely considered pointwise conditions in the sense that they allow solutions to have singularities, and different from other conditions given by integrals with a singular kernel since they arise from well-defined initial value problems. We derive Lyapunov-type inequalities for linear fractional differential equations and apply them to establish nonexistence, uniqueness, and existence-uniqueness of solutions for certain linear fractional boundary value problems. Parallel results are also obtained for sequential fractional differential equations. An example is given to show how computer programs and numerical algorithms can be used to verify the conditions and to apply the results. |
| first_indexed | 2024-04-09T13:38:57Z |
| format | Article |
| id | doaj.art-fdbf25967ca540738d46ba44c462c02f |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:38:57Z |
| publishDate | 2016-06-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-fdbf25967ca540738d46ba44c462c02f2023-05-09T07:53:05ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752016-06-0120164311610.14232/ejqtde.2016.1.434879Fractional boundary value problems and Lyapunov-type inequalities with fractional integral boundary conditionsSougata Dhar0Qingkai Kong1Michael McCabe2Northern Illinois Uinversity, DeKalb, IL, U.S.A.Northern Illinois University, DeKalb, IL, U.S.A.Northern Illinois Uinversity, DeKalb, IL, U.S.A.We discuss boundary value problems for Riemann-Liouville fractional differential equations with certain fractional integral boundary conditions. Such boundary conditions are different from the widely considered pointwise conditions in the sense that they allow solutions to have singularities, and different from other conditions given by integrals with a singular kernel since they arise from well-defined initial value problems. We derive Lyapunov-type inequalities for linear fractional differential equations and apply them to establish nonexistence, uniqueness, and existence-uniqueness of solutions for certain linear fractional boundary value problems. Parallel results are also obtained for sequential fractional differential equations. An example is given to show how computer programs and numerical algorithms can be used to verify the conditions and to apply the results.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4879fractional differential equationsfractional integral boundary conditionslyapunov-type inequalitiesboundary value problemsexistence and uniqueness of solutions |
| spellingShingle | Sougata Dhar Qingkai Kong Michael McCabe Fractional boundary value problems and Lyapunov-type inequalities with fractional integral boundary conditions Electronic Journal of Qualitative Theory of Differential Equations fractional differential equations fractional integral boundary conditions lyapunov-type inequalities boundary value problems existence and uniqueness of solutions |
| title | Fractional boundary value problems and Lyapunov-type inequalities with fractional integral boundary conditions |
| title_full | Fractional boundary value problems and Lyapunov-type inequalities with fractional integral boundary conditions |
| title_fullStr | Fractional boundary value problems and Lyapunov-type inequalities with fractional integral boundary conditions |
| title_full_unstemmed | Fractional boundary value problems and Lyapunov-type inequalities with fractional integral boundary conditions |
| title_short | Fractional boundary value problems and Lyapunov-type inequalities with fractional integral boundary conditions |
| title_sort | fractional boundary value problems and lyapunov type inequalities with fractional integral boundary conditions |
| topic | fractional differential equations fractional integral boundary conditions lyapunov-type inequalities boundary value problems existence and uniqueness of solutions |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4879 |
| work_keys_str_mv | AT sougatadhar fractionalboundaryvalueproblemsandlyapunovtypeinequalitieswithfractionalintegralboundaryconditions AT qingkaikong fractionalboundaryvalueproblemsandlyapunovtypeinequalitieswithfractionalintegralboundaryconditions AT michaelmccabe fractionalboundaryvalueproblemsandlyapunovtypeinequalitieswithfractionalintegralboundaryconditions |