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Existence of a unique weak solution to a nonlinear non-autonomous time-fractional wave equation (of distributed-order)

Karel Van Bockstal (UGent)
(2020) MATHEMATICS. 8(8).
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Abstract
We study an initial-boundary value problem for a fractional wave equation of time distributed-order with a nonlinear source term. The coefficients of the second order differential operator are dependent on the spatial and time variables. We show the existence of a unique weak solution to the problem under low regularity assumptions on the data, which includes weakly singular solutions in the class of admissible problems. A similar result holds true for the fractional wave equation with Caputo fractional derivative.
Keywords
DIFFERENCE-SCHEMES, time-fractional wave equation, distributed-order, non-autonomous, time, discretization, existence, uniqueness

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MLA
Van Bockstal, Karel. “Existence of a Unique Weak Solution to a Nonlinear Non-Autonomous Time-Fractional Wave Equation (of Distributed-Order).” MATHEMATICS, vol. 8, no. 8, 2020, doi:10.3390/math8081283.
APA
Van Bockstal, K. (2020). Existence of a unique weak solution to a nonlinear non-autonomous time-fractional wave equation (of distributed-order). MATHEMATICS, 8(8). https://doi.org/10.3390/math8081283
Chicago author-date
Van Bockstal, Karel. 2020. “Existence of a Unique Weak Solution to a Nonlinear Non-Autonomous Time-Fractional Wave Equation (of Distributed-Order).” MATHEMATICS 8 (8). https://doi.org/10.3390/math8081283.
Chicago author-date (all authors)
Van Bockstal, Karel. 2020. “Existence of a Unique Weak Solution to a Nonlinear Non-Autonomous Time-Fractional Wave Equation (of Distributed-Order).” MATHEMATICS 8 (8). doi:10.3390/math8081283.
Vancouver
1.
Van Bockstal K. Existence of a unique weak solution to a nonlinear non-autonomous time-fractional wave equation (of distributed-order). MATHEMATICS. 2020;8(8).
IEEE
[1]
K. Van Bockstal, “Existence of a unique weak solution to a nonlinear non-autonomous time-fractional wave equation (of distributed-order),” MATHEMATICS, vol. 8, no. 8, 2020.
@article{8686405,
  abstract     = {{We study an initial-boundary value problem for a fractional wave equation of time distributed-order with a nonlinear source term. The coefficients of the second order differential operator are dependent on the spatial and time variables. We show the existence of a unique weak solution to the problem under low regularity assumptions on the data, which includes weakly singular solutions in the class of admissible problems. A similar result holds true for the fractional wave equation with Caputo fractional derivative.}},
  articleno    = {{1283}},
  author       = {{Van Bockstal, Karel}},
  issn         = {{2227-7390}},
  journal      = {{MATHEMATICS}},
  keywords     = {{DIFFERENCE-SCHEMES,time-fractional wave equation,distributed-order,non-autonomous,time,discretization,existence,uniqueness}},
  language     = {{eng}},
  number       = {{8}},
  pages        = {{16}},
  title        = {{Existence of a unique weak solution to a nonlinear non-autonomous time-fractional wave equation (of distributed-order)}},
  url          = {{http://doi.org/10.3390/math8081283}},
  volume       = {{8}},
  year         = {{2020}},
}
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