An operator-based approach for the construction of closed-form solutions to fractional differential equations
An operator-based approach for the construction of closed-form solutions to fractional differential equations is presented in this paper. The technique is based on the analysis of Caputo and Riemann-Liouville algebras of fractional power series. Explicit solutions to a class of linear fractional dif...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2018-10-01
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| Series: | Mathematical Modelling and Analysis |
| Subjects: | |
| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/302 |
| _version_ | 1818888299271421952 |
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| author | Zenonas Navickas Tadas Telksnys Inga Timofejeva Romas Marcinkevičius Minvydas Ragulskis |
| author_facet | Zenonas Navickas Tadas Telksnys Inga Timofejeva Romas Marcinkevičius Minvydas Ragulskis |
| author_sort | Zenonas Navickas |
| collection | DOAJ |
| description | An operator-based approach for the construction of closed-form solutions to fractional differential equations is presented in this paper. The technique is based on the analysis of Caputo and Riemann-Liouville algebras of fractional power series. Explicit solutions to a class of linear fractional differential equations are obtained in terms of Mittag-Leffler and fractionally-integrated exponential functions in order to demonstrate the viability of the proposed technique. |
| first_indexed | 2024-12-19T16:50:55Z |
| format | Article |
| id | doaj.art-6662dc9b046040fab2a5f043ec83658c |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-19T16:50:55Z |
| publishDate | 2018-10-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-6662dc9b046040fab2a5f043ec83658c2022-12-21T20:13:32ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102018-10-0123410.3846/mma.2018.040An operator-based approach for the construction of closed-form solutions to fractional differential equationsZenonas Navickas0Tadas Telksnys1Inga Timofejeva2Romas Marcinkevičius3Minvydas Ragulskis4Kaunas University of TechnologyKaunas University of TechnologyKaunas University of TechnologyKaunas University of TechnologyKaunas University of TechnologyAn operator-based approach for the construction of closed-form solutions to fractional differential equations is presented in this paper. The technique is based on the analysis of Caputo and Riemann-Liouville algebras of fractional power series. Explicit solutions to a class of linear fractional differential equations are obtained in terms of Mittag-Leffler and fractionally-integrated exponential functions in order to demonstrate the viability of the proposed technique.https://journals.vgtu.lt/index.php/MMA/article/view/302fractional differential equationoperator calculusanalytical solutionclosed-form solution |
| spellingShingle | Zenonas Navickas Tadas Telksnys Inga Timofejeva Romas Marcinkevičius Minvydas Ragulskis An operator-based approach for the construction of closed-form solutions to fractional differential equations Mathematical Modelling and Analysis fractional differential equation operator calculus analytical solution closed-form solution |
| title | An operator-based approach for the construction of closed-form solutions to fractional differential equations |
| title_full | An operator-based approach for the construction of closed-form solutions to fractional differential equations |
| title_fullStr | An operator-based approach for the construction of closed-form solutions to fractional differential equations |
| title_full_unstemmed | An operator-based approach for the construction of closed-form solutions to fractional differential equations |
| title_short | An operator-based approach for the construction of closed-form solutions to fractional differential equations |
| title_sort | operator based approach for the construction of closed form solutions to fractional differential equations |
| topic | fractional differential equation operator calculus analytical solution closed-form solution |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/302 |
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