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Thermoelasticity Based on Space-Time-Fractional Heat Conduction Equation

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

Abstract

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.

Keywords

Stress Tensor Cauchy Problem Fundamental Solution Fractional Derivative Heat Conduction Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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