Fractional telegraph equation under moving time-harmonic impact

Yuriy Povstenko, Martin Ostoja-Starzewski

Research output: Contribution to journalArticlepeer-review


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<α<2. 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 considered problem is solved using the integral transforms technique. The solution to the “wave-type” equation contains wave fronts and describes the Doppler effect contrary to the solution for the “heat-type” equation. Numerical results are illustrated graphically for different values of nondimensional parameters.

Original languageEnglish (US)
Article number121958
JournalInternational Journal of Heat and Mass Transfer
StatePublished - Jan 2022


  • Caputo derivative
  • Fourier transform
  • Fractional calculus
  • Laplace transform
  • Telegraph equation
  • Time-harmonic impact

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes


Dive into the research topics of 'Fractional telegraph equation under moving time-harmonic impact'. Together they form a unique fingerprint.

Cite this