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Thermoelasticity Based on Space-Time-Fractional Heat Conduction Equation

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Fractional Thermoelasticity

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 219))

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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.

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Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Jan Długosz University, Częstochowa, Poland

    Yuriy Povstenko

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  1. Yuriy Povstenko
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Correspondence to Yuriy Povstenko .

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Povstenko, Y. (2015). Thermoelasticity Based on Space-Time-Fractional Heat Conduction Equation. In: Fractional Thermoelasticity. Solid Mechanics and Its Applications, vol 219. Springer, Cham. https://doi.org/10.1007/978-3-319-15335-3_6

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  • DOI: https://doi.org/10.1007/978-3-319-15335-3_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-15334-6

  • Online ISBN: 978-3-319-15335-3

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