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Harmonic impact on the surface of a half-plane in the framework of Time-Fractional Heat Conduction

Povstenko Y.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2016

Vol. 21

85--92

The time-fractional heat conduction equation with the Caputo derivative is considered in a half-plane. The boundary value of temperature varies harmonically in time. The integral transform technique is used; the solution is obtained in terms of integral with integrand being the Mittag-Leffler functions. The particular case of solution corresponding to the classical heat conduction equation is discussed in details.