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An axisymmetric problem for Gaussian-distributed heating of a lateral surface of an infinite cylinder is solved in the framework of fractional thermoelasticity based on the timefractional heat conduction equation with the Caputo derivative. The representation of stresses in terms of displacement potential and Love function is used to satisfy the boundary conditions on a surface of a cylinder. The results of numerical calculation are presented for different values of the order of fractional derivative and nondimensional time.

Thermal stresses in a long cylinder under Gaussian-distributed heating in the framework of fractional thermoelasticity