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On a non-local problem for a multi-term fractional diffusion-wave equation

Michael Ruzhansky (UGent) , Niyaz Tokmagambetov (UGent) and Berikbol Torebek (UGent)
(2020) FRACTIONAL CALCULUS AND APPLIED ANALYSIS. 23(2). p.324-355
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Abstract
This paper deals with the multi-term generalisation of the time-fractional diffusion-wave equation for general operators with discrete spectrum, as well as for positive hypoelliptic operators, with homogeneous multi-point time-nonlocal conditions. Several examples of the settings where our nonlocal problems are applicable are given. The results for the discrete spectrum are also applied to treat the case of general homogeneous hypoelliptic left-invariant differential operators on general graded Lie groups, by using the representation theory of the group. For all these problems, we show the existence, uniqueness, and the explicit representation formulae for the solutions.
Keywords
Applied Mathematics, Analysis, time-fractional diffusion-wave equation, Caputo derivative, noanlocal-initial problem, multivariate Mittag-Leffler function, self-adjoint operator, BOUNDARY-VALUE-PROBLEMS, WEAK SOLUTIONS, OPERATORS, PRINCIPLE

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MLA
Ruzhansky, Michael, et al. “On a Non-Local Problem for a Multi-Term Fractional Diffusion-Wave Equation.” FRACTIONAL CALCULUS AND APPLIED ANALYSIS, vol. 23, no. 2, 2020, pp. 324–55, doi:10.1515/fca-2020-0016.
APA
Ruzhansky, M., Tokmagambetov, N., & Torebek, B. (2020). On a non-local problem for a multi-term fractional diffusion-wave equation. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 23(2), 324–355. https://doi.org/10.1515/fca-2020-0016
Chicago author-date
Ruzhansky, Michael, Niyaz Tokmagambetov, and Berikbol Torebek. 2020. “On a Non-Local Problem for a Multi-Term Fractional Diffusion-Wave Equation.” FRACTIONAL CALCULUS AND APPLIED ANALYSIS 23 (2): 324–55. https://doi.org/10.1515/fca-2020-0016.
Chicago author-date (all authors)
Ruzhansky, Michael, Niyaz Tokmagambetov, and Berikbol Torebek. 2020. “On a Non-Local Problem for a Multi-Term Fractional Diffusion-Wave Equation.” FRACTIONAL CALCULUS AND APPLIED ANALYSIS 23 (2): 324–355. doi:10.1515/fca-2020-0016.
Vancouver
1.
Ruzhansky M, Tokmagambetov N, Torebek B. On a non-local problem for a multi-term fractional diffusion-wave equation. FRACTIONAL CALCULUS AND APPLIED ANALYSIS. 2020;23(2):324–55.
IEEE
[1]
M. Ruzhansky, N. Tokmagambetov, and B. Torebek, “On a non-local problem for a multi-term fractional diffusion-wave equation,” FRACTIONAL CALCULUS AND APPLIED ANALYSIS, vol. 23, no. 2, pp. 324–355, 2020.
@article{8665299,
  abstract     = {{This paper deals with the multi-term generalisation of the time-fractional diffusion-wave equation for general operators with discrete spectrum, as well as for positive hypoelliptic operators, with homogeneous multi-point time-nonlocal conditions. Several examples of the settings where our nonlocal problems are applicable are given. The results for the discrete spectrum are also applied to treat the case of general homogeneous hypoelliptic left-invariant differential operators on general graded Lie groups, by using the representation theory of the group. For all these problems, we show the existence, uniqueness, and the explicit representation formulae for the solutions.}},
  author       = {{Ruzhansky, Michael and Tokmagambetov, Niyaz and Torebek, Berikbol}},
  issn         = {{1311-0454}},
  journal      = {{FRACTIONAL CALCULUS AND APPLIED ANALYSIS}},
  keywords     = {{Applied Mathematics,Analysis,time-fractional diffusion-wave equation,Caputo derivative,noanlocal-initial problem,multivariate Mittag-Leffler function,self-adjoint operator,BOUNDARY-VALUE-PROBLEMS,WEAK SOLUTIONS,OPERATORS,PRINCIPLE}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{324--355}},
  title        = {{On a non-local problem for a multi-term fractional diffusion-wave equation}},
  url          = {{http://dx.doi.org/10.1515/fca-2020-0016}},
  volume       = {{23}},
  year         = {{2020}},
}
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