FRACTIONAL HEAT CONDUCTION EQUATION AND ASSOCIATED THERMAL STRESS

By Yuriy Povstenko. 2004

597 citations recorded by the source corpus.

Subfields: Mechanics of Materials, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/4051e73e1f0c633698b0ca6e8c640213c92ac3fc

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In Mechanics of Materials

In Modeling and Simulation

Citations in the corpus

Fractional Cattaneo-Type Equations and Generalized Thermoelasticity (2011, methodology): “The proposed theory, on the one hand, interpolates the theory of Lord and Shulman [20] ( = 0 = 1) and thermoelasticity without energy dissipation of Green and Naghdi [13] ( = 2), and on the other hand, generalizes the theory of thermal stresses based on fractional heat conduction equation [15].”
Fractional Order Theory of Thermoelastic Diffusion (2011, methodology): “A quasi-static uncoupled theory of thermoelasticity based on fractional heat conduction equation was put forward by Povstenko [ 32 ].”
Generalized thermoelasticity with memory-dependent derivatives involving two temperatures (2016, background): “Ezzat and El-Karamany solved a one-dimensional model of the two-temperature generalized magneto-thermo-elasticity theory with two relaxation times in a perfect electric conducting medium [14].”
Thermoelasticity that uses fractional heat conduction equation (2009, methodology): “Within the framework of the proposed theories, several thermoelastic problems were considered [ 55 , 56, 58, 59, 61] (see also [60]).”
Nonlocal theory of thermoelastic materials with voids and fractional derivative heat transfer (2019, background): “In the last few years, fractional calculus has been successfully applied to extend generalized thermoelasticity theories to fractional order generalized thermoelasticity by Bachher et al. [33,34], Povstenko [35,36], Sherief [37], Youssef [38], Ezzat and his co-workers [39–43] etc. Rossikhin and Shit”
Size-dependent generalized thermoelasticity using Eringen's nonlocal model (2015, background): “Recently, inspired by fractional calculus increasing investigation, especially, its successful application in anomalous diffusion, generalized thermoelasticity models have been further extended into fractional ones (Povstenko, 2004; Youssef, 2010; Ezzat, 2011; Yu et al., 2013) to express memory-depe”
Fractal heat conduction problem solved by local fractional variation iteration method (2013, methodology): “In these cases the fractional calculus assuming smooth functions [9-15] due to the continuum concept and the memory effects is not applicable.”