Journal ArticleDOI
Fractional heat conduction equation and associated thermal stress
TLDR
A quasi-static uncoupled theory of thermoelasticity based on the heat conduction equation with a time-fractional derivative of order α is proposed in this article.Abstract:
A quasi-static uncoupled theory of thermoelasticity based on the heat conduction equation with a time-fractional derivative of order α is proposed. Because the heat conduction equation in the case 1≤α≤2 interpolates the parabolic equation (α = 1) and the wave equation (α = 2), the proposed theory interpolates a classical thermoelasticity and a thermoelasticity without energy dissipation introduced by Green and Naghdi. The Caputo fractional derivative is used. The stresses corresponding to the fundamental solutions of a Cauchy problem for the fractional heat conduction equation are found in one-dimensional and two-dimensional cases.read more
Citations
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Journal ArticleDOI
I and i
TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
Journal ArticleDOI
Fractal heat conduction problem solved by local fractional variation iteration method
Xiao-Jun Yang,Dumitru Baleanu +1 more
TL;DR: In this article, a local fractional variational iteration method for processing the local heat conduction equation arising in fractal heat transfer is presented. But the method is not suitable for the case of large-scale heat transfer.
Journal ArticleDOI
Fractional catteneo-type equations and generalized thermoelasticity
TL;DR: In this paper, the generalized Cattaneo-type equations with time-fractional derivatives are considered and the corresponding theory of thermal stresses is formulated, interpolating the theory of Lord and Shulman and thermoelasticity without energy dissipation of Green and Naghdi.
References
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Journal ArticleDOI
Handbook of Mathematical Functions
Journal ArticleDOI
I and i
TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
Book
An Introduction to the Fractional Calculus and Fractional Differential Equations
Kenneth S. Miller,Bertram Ross +1 more
TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.