Thermoelasticity Based on Space-Time-Fractional Heat Conduction Equation

In this chapter, we consider theory of thermal stresses based on the space-time fractional heat conduction equationFractional heat conduction equation with the Caputo fractional derivative with respect to time describing time-nonlocality and the fractional Laplace operator (Riesz operatorRiesz operator) with respect to spatial variables describing space-nonlocality. Fundamental solutions to the Cauchy and source problemsSource problem for axisymmetric equation in polar and cylindrical coordinatesCylindrical coordinates and central symmetric equation in spherical coordinatesSpherical coordinates are obtained using the integral transform technique. Numerical results are illustrated graphically for different values of orders of time- and space-fractional derivatives.