| Title |
The extension of analytic solutions to FDEs to the negative half-line / |
| Authors |
Timofejeva, Inga ; Navickas, Zenonas ; Telksnys, Tadas ; Marcinkevičius, Romas ; Yang, Xiao-Jun ; Ragulskis, Minvydas |
| DOI |
10.3934/math.2021195 |
| Full Text |
|
| Is Part of |
AIMS Mathematics.. Springfield, MO : American institute of mathematical sciences. 2021, vol. 6, iss. 4, p. 3257-3271.. ISSN 2473-6988 |
| Keywords [eng] |
fractional differential equation ; operator calculus ; negative half-line ; solitary wave ; inverse balancing |
| Abstract [eng] |
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 sucient 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. |
| Published |
Springfield, MO : American institute of mathematical sciences |
| Type |
Journal article |
| Language |
English |
| Publication date |
2021 |
| CC license |
|
