Thermoelasticity Based on Space-Time-Fractional Heat Conduction Equation

  • Yuriy PovstenkoEmail author
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 219)


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


Stress Tensor Cauchy Problem Fundamental Solution Fractional Derivative Heat Conduction Equation 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute of Mathematics and Computer ScienceJan Długosz UniversityCzęstochowaPoland

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