The extension of analytic solutions to FDEs to the negative half-line
An analytical framework for the extension of solutions to fractional differential equations (FDEs) to the negative half-line is presented in this paper. The proposed technique is based on the construction of a special characteristic equation corresponding to the original FDE (when the characteristic...
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AIMS Press
2021-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | http://www.aimspress.com/article/doi/10.3934/math.2021195?viewType=HTML |
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| author | Inga Timofejeva Zenonas Navickas Tadas Telksnys Romas Marcinkevičius Xiao-Jun Yang Minvydas Ragulskis |
| author_facet | Inga Timofejeva Zenonas Navickas Tadas Telksnys Romas Marcinkevičius Xiao-Jun Yang Minvydas Ragulskis |
| author_sort | Inga Timofejeva |
| collection | DOAJ |
| description | An analytical framework for the extension of solutions to fractional differential equations (FDEs) to the negative half-line is presented in this paper. The proposed technique is based on the construction of a special characteristic equation corresponding to the original FDE (when the characteristic equation does exist). This characteristic equation enables the construction analytic solutions to FDEs are expressed in the form of infinite fractional power series. Necessary and sufficient conditions for the existence of such an extension are discussed in detail. It is demonstrated that the extension of solutions to FDEs to the negative half-line is not a single-valued operation. Computational experiments are used to illustrate the efficacy of the proposed scheme. |
| first_indexed | 2024-12-16T11:32:42Z |
| format | Article |
| id | doaj.art-590b263c24b14ce5a5e7a9dc7fd7a6c7 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-16T11:32:42Z |
| publishDate | 2021-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-590b263c24b14ce5a5e7a9dc7fd7a6c72022-12-21T22:33:12ZengAIMS PressAIMS Mathematics2473-69882021-01-01643257327110.3934/math.2021195The extension of analytic solutions to FDEs to the negative half-lineInga Timofejeva0Zenonas Navickas1Tadas Telksnys2Romas Marcinkevičius3Xiao-Jun Yang4Minvydas Ragulskis 51. Center for Nonlinear Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, Lithuania1. Center for Nonlinear Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, Lithuania 1. Center for Nonlinear Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, Lithuania2. Department of Software Engineering, Kaunas University of Technology, Studentu 50-415, Kaunas LT-51368, Lithuania3. School of Mathematics and State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, No.1, Daxue Road, Xuzhou 221116, Jiangsu, P. R. China1. Center for Nonlinear Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, LithuaniaAn analytical framework for the extension of solutions to fractional differential equations (FDEs) to the negative half-line is presented in this paper. The proposed technique is based on the construction of a special characteristic equation corresponding to the original FDE (when the characteristic equation does exist). This characteristic equation enables the construction analytic solutions to FDEs are expressed in the form of infinite fractional power series. Necessary and sufficient conditions for the existence of such an extension are discussed in detail. It is demonstrated that the extension of solutions to FDEs to the negative half-line is not a single-valued operation. Computational experiments are used to illustrate the efficacy of the proposed scheme.http://www.aimspress.com/article/doi/10.3934/math.2021195?viewType=HTMLfractional differential equationoperator calculusnegative half-linesolitary waveinverse balancing |
| spellingShingle | Inga Timofejeva Zenonas Navickas Tadas Telksnys Romas Marcinkevičius Xiao-Jun Yang Minvydas Ragulskis The extension of analytic solutions to FDEs to the negative half-line AIMS Mathematics fractional differential equation operator calculus negative half-line solitary wave inverse balancing |
| title | The extension of analytic solutions to FDEs to the negative half-line |
| title_full | The extension of analytic solutions to FDEs to the negative half-line |
| title_fullStr | The extension of analytic solutions to FDEs to the negative half-line |
| title_full_unstemmed | The extension of analytic solutions to FDEs to the negative half-line |
| title_short | The extension of analytic solutions to FDEs to the negative half-line |
| title_sort | extension of analytic solutions to fdes to the negative half line |
| topic | fractional differential equation operator calculus negative half-line solitary wave inverse balancing |
| url | http://www.aimspress.com/article/doi/10.3934/math.2021195?viewType=HTML |
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