Fractional heat conduction in a space with a source varying harmonically in time and associated thermal stresses

摘要

Time-nonlocal generalization of the classical Fourier law with the long-tail power kernel can be interpreted in terms of fractional calculus (theory of integrals and derivatives of noninteger order) and leads to the time-fractional heat conduction equation with the Caputo derivative. Fractional heat conduction equation with the harmonic source term under zero initial conditions is studied. Different formulations of the problem for the standard parabolic heat conduction equation and for the hyperbolic wave equation appearing in thermoelasticity without energy dissipation are discussed. The integral transform technique is used. The corresponding thermal stresses are found using the displacement potential.