# Time-Fractional Heat Conduction with Heat Absorption in a Half-Line Domain Due to Boundary Value of the Heat Flux Varying Harmonically in Time

• Yuriy Povstenko
• Tamara Kyrylych
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 559)

## Abstract

The time-fractional heat conduction equation with heat absorption is considered in a half-line domain under the mathematical and physical Neumann boundary conditions varying harmonically in time. The Caputo derivative is employed. The Laplace transform with respect to time and the cos-Fourier transform with respect to the spatial coordinate are used. The solutions are obtained in terms of integrals with integrands being the Mittag-Leffler functions. The numerical results are illustrated graphically.

## Keywords

Fractional calculus Caputo derivative Harmonic impact Mittag-Leffler function

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