Fractional telegraph equation under moving time-harmonic impact

•The time-fractional telegraph equation with moving time-harmonic source is considered on a real line.•Two characteristic versions of this equation: the “wave-type” with the second and Caputo fractional time-derivatives as well as the “heat-type” with the first and Caputo fractional time-derivatives...

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Veröffentlicht in:International journal of heat and mass transfer 2022-01, Vol.182, p.121958, Article 121958
Hauptverfasser: Povstenko, Yuriy, Ostoja-Starzewski, Martin
Format: Artikel
Sprache:eng
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Zusammenfassung:•The time-fractional telegraph equation with moving time-harmonic source is considered on a real line.•Two characteristic versions of this equation: the “wave-type” with the second and Caputo fractional time-derivatives as well as the “heat-type” with the first and Caputo fractional time-derivatives are investigated.•The solution to the “wave-type” equation contains wave fronts and describes the Doppler effect contrary to the solution for the “heat-type” equation.•For the time-fractional telegraph equation it is impossible to consider the quasi-steady-state corresponding to the solution being a product of a function of the spatial coordinate and the time-harmonic term.•The derived solutions can be successfully used when the source term can be expanded into a Fourier series. The time-fractional telegraph equation with moving time-harmonic source is considered on a real line. We investigate two characteristic versions of this equation: the “wave-type” with the second and Caputo fractional time-derivatives as well as the “heat-type” with the first and Caputo fractional time-derivatives. In both cases the order of fractional derivative 1
ISSN:0017-9310
1879-2189
DOI:10.1016/j.ijheatmasstransfer.2021.121958