Space-dependent variable-order time-fractional wave equation : existence and uniqueness of its weak solution
- Author
- Karel Van Bockstal (UGent) , A.S. Hendy and M.A. Zaky
- Organization
- Project
- Abstract
- The investigation of an initial-boundary value problem for a fractional wave equation with space-dependent variable-order wherein the coefficients have a dependency on the spatial and time variables is the concern of this work. This type of variable-order fractional differential operator originates in the modelling of viscoelastic materials. The global in time existence of a unique weak solution to the model problem has been proved under appropriate conditions on the data. Rothe's time discretization method is applied to achieve that purpose.
- Keywords
- Mathematics (miscellaneous), Time fractional wave equation, variable coefficients, uniqueness and existence, non-autonomous, variable-order, Rothe's time discretization, DIFFERENTIAL-EQUATIONS, REGULARITY
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-01GP0KPQRNW305VW47DXQ3TPXP
- MLA
- Van Bockstal, Karel, et al. “Space-Dependent Variable-Order Time-Fractional Wave Equation : Existence and Uniqueness of Its Weak Solution.” QUAESTIONES MATHEMATICAE, vol. 46, no. 8, 2023, pp. 1695–715, doi:10.2989/16073606.2022.2110959.
- APA
- Van Bockstal, K., Hendy, A. S., & Zaky, M. A. (2023). Space-dependent variable-order time-fractional wave equation : existence and uniqueness of its weak solution. QUAESTIONES MATHEMATICAE, 46(8), 1695–1715. https://doi.org/10.2989/16073606.2022.2110959
- Chicago author-date
- Van Bockstal, Karel, A.S. Hendy, and M.A. Zaky. 2023. “Space-Dependent Variable-Order Time-Fractional Wave Equation : Existence and Uniqueness of Its Weak Solution.” QUAESTIONES MATHEMATICAE 46 (8): 1695–1715. https://doi.org/10.2989/16073606.2022.2110959.
- Chicago author-date (all authors)
- Van Bockstal, Karel, A.S. Hendy, and M.A. Zaky. 2023. “Space-Dependent Variable-Order Time-Fractional Wave Equation : Existence and Uniqueness of Its Weak Solution.” QUAESTIONES MATHEMATICAE 46 (8): 1695–1715. doi:10.2989/16073606.2022.2110959.
- Vancouver
- 1.Van Bockstal K, Hendy AS, Zaky MA. Space-dependent variable-order time-fractional wave equation : existence and uniqueness of its weak solution. QUAESTIONES MATHEMATICAE. 2023;46(8):1695–715.
- IEEE
- [1]K. Van Bockstal, A. S. Hendy, and M. A. Zaky, “Space-dependent variable-order time-fractional wave equation : existence and uniqueness of its weak solution,” QUAESTIONES MATHEMATICAE, vol. 46, no. 8, pp. 1695–1715, 2023.
@article{01GP0KPQRNW305VW47DXQ3TPXP,
abstract = {{The investigation of an initial-boundary value problem for a fractional wave equation with space-dependent variable-order wherein the coefficients have a dependency on the spatial and time variables is the concern of this work. This type of variable-order fractional differential operator originates in the modelling of viscoelastic materials. The global in time existence of a unique weak solution to the model problem has been proved under appropriate conditions on the data. Rothe's time discretization method is applied to achieve that purpose.}},
author = {{Van Bockstal, Karel and Hendy, A.S. and Zaky, M.A.}},
issn = {{1607-3606}},
journal = {{QUAESTIONES MATHEMATICAE}},
keywords = {{Mathematics (miscellaneous),Time fractional wave equation,variable coefficients,uniqueness and existence,non-autonomous,variable-order,Rothe's time discretization,DIFFERENTIAL-EQUATIONS,REGULARITY}},
language = {{eng}},
number = {{8}},
pages = {{1695--1715}},
title = {{Space-dependent variable-order time-fractional wave equation : existence and uniqueness of its weak solution}},
url = {{http://doi.org/10.2989/16073606.2022.2110959}},
volume = {{46}},
year = {{2023}},
}
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