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The extension of analytic solutions to FDEs to the negative half-line

  • Received: 14 October 2020 Accepted: 31 December 2020 Published: 15 January 2021
  • MSC : 34A08, 34A25, 26A33

  • 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.

    Citation: 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[J]. AIMS Mathematics, 2021, 6(4): 3257-3271. doi: 10.3934/math.2021195

    Related Papers:

  • 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.


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