References
- Ezzat MA, Zakaria M, El-Bary AA. Thermo-electric-visco-elastic material. J. Appl. Poly. Sci. 2010;117:1934–1944.10.1002/app.v117:4
- Predeleanu PM. On thermal stresses in visco-elastic bodies. Bull. Math. Soc. Phys., R.P.R. 1959; 2,3.
- Fung YC. Foundations of solid mechanics. Englewood Cliffs, NJ: Prentice-Hall; 1968.
- Gross B. Mathematical structure of the theories of viscoelasticity. Paris: Hemann; 1953.
- Staverman AJ, Schwarzl F. Bruchspannung und Festigkeit von Hochpolymeren. In Stuart HA, editor. Die physik der hochpolymeren [The physics of high polymer]. Vol. 4, Chapter 1. Springer Verlag; 1956.
- Alfery T, Gurnee EF. In: Eirich FR, editor. Rheology: theory and applications. Vol. 1. New York (NY): Academic Press; 1956.
- Ferry JD. Viscoelastic properties of polymers. New York (NY): Wiley; 1977.
- Ilioushin AA, Pobedria BE. Fundamentals of the mathematical theory of thermal viscoelasticity. Moscow: Nauka; 1970. Russian.
- Pobedria BE. Coupled problems in continuum mechanics. J. Durab. Plast. 1984;2:224–253.
- Biot M. Thermoelasticity and irreversible thermodynamics. J. Appl. Phys. 1956;27:240–253.10.1063/1.1722351
- Ignaczak J. Generalized thermoelasticity and its applications. In: Hetnarski RB, editor. Thermal stresses III. New York (NY): Elsevier; 1989. p. 279–354.
- Chandrasekharaiah DS. Hyperbolic thermoelasticity: a review of recent literature. Appl Mech Rev. 1998;51:705–729.10.1115/1.3098984
- Hetnarski RB, Ignaczak J. Generalized thermoelasticity. J. Therm. Stress. 1999;22:451–476.
- Hetnarski RB, Eslami MR. Thermal stresses, advanced theory and applications. New York (NY): Springer; 2009.
- Lord H, Shulman Y. A generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solid. 1967;15:299–309.10.1016/0022-5096(67)90024-5
- Ignaczak J, Ostoja-Starzewski M. Thermoelasticity with finite wave speeds. New York (NY): Oxford University Press; 2009.10.1093/acprof:oso/9780199541645.001.0001
- Joseph D, Preziosi L. Heat waves. Rev. Mod. Phys. 1989;61:41–73.10.1103/RevModPhys.61.41
- Cattaneo C. Sur une forme de l’équation de la Chaleur éliminant le paradoxe d’une propagation instantaneée. C.R. Acad. Sci. 1958;247:431–433.
- Ignaczak J. Uniqueness in generalized thermoelasticity. J. Therm. Stress. 1979;2:171–175.10.1080/01495737908962399
- Chandrasekharaiah DS. A uniqueness theorem in the theory of thermoelasticity without energy dissipation. J. Therm. Stress. 1996;19:267–272.10.1080/01495739608946173
- Sherief HH. On uniqueness and stability in generalized thermoelasticity. Quar. J. Appl. Math. 1987;45:773–778.
- Ezzat MA, El-Karamany AS. The uniqueness and reciprocity theorems for generalized thermoviscoelasticity for anisotropic media. J. Therm. Stress. 2002;25:507–522.
- Ezzat MA, El-Karamany AS. On uniqueness and reciprocity theorems for generalized thermo-viscoelasticity with thermal relaxation. Can. J. Phys. 2003;81:823–833.10.1139/p03-070
- Sherief HH. Fundamental solution of generalized thermoelastic problem for short times. J. Therm. Stress. 1986;9:151–164.10.1080/01495738608961894
- Ezzat MA. Fundamental solution in generalized magneto-thermoelasticity with two relaxation times for perfect conductor cylindrical region. Int. J. Eng. Sci. 2004;42:1503–1519.10.1016/j.ijengsci.2003.09.013
- Ezzat MA, El-Karamany AS. Propagation of discontinuities in magneto-thermoelastic half-space. J. Therm. Stress. 2006;29:331–358.10.1080/01495730500360526
- El-Karamany AS, Ezzat MA. Discontinuities in generalized thermo-viscoelasticity under four theories. J. Therm. Stress. 2004;27:1187–1212.10.1080/014957390523598
- Chen PJ, Gurtin ME. On a theory of heat conduction involving two temperatures. Z. Angew. Math. Phys. 1968;19:614–627.10.1007/BF01594969
- Chen PJ, Gurtin ME, Williams WO. A note on nonsimple heat conduction. Z. Angew. Math. Phys. 1968;19:969–970.
- Chen PJ, Gurtin ME, Williams WO. On the thermodynamics of non-simple elastic materials with two temperatures. Z. Angew. Math. Phys. 1969;20:107–112.10.1007/BF01591120
- Warren WE, Chen PJ. Wave propagation in the two-temperature theory of thermoelasticity. Acta Mech. 1973;16:21–33.10.1007/BF01177123
- Boley BA, Tolins IS. Transient coupled thermoplastic boundary value problems in the half space. J. Appl. Mech. 1962;29:637–646.10.1115/1.3640647
- Ieşan D. On the linear coupled thermoelasticity with two temperatures. Z. Angew. Math. Phys. 1970;21:583–591.10.1007/BF01587687
- Youssef HM. Theory of two-temperature generalized thermoelasticity. IMA J. Appl. Math. 2006;71:383–390.10.1093/imamat/hxh101
- Magaña A, Quintanilla R. Uniqueness and growth of solutions in two-temperature generalized thermoelastic theories. Math. Mech. Solids. 2009;14:622–634.10.1177/1081286507087653
- Knopoff L. The Interaction between elastic wave motion and a magnetic field in electrical conductors. J. Geophys. Res. 1955;60:441–456.10.1029/JZ060i004p00441
- Baqir MA, Choudhury PK. Electromagnetic waves in perfect electromagnetic Conductor loaded uniaxial anisotropic chiral metamaterial waveguide. In: Proceedings – 2012 6th Asia-Pacific Conference on Environmental Electromagnetics, CEEM 2012; 2012 Nov 6–9; IEEE, Shanghai. p. 104–107. doi:10.1109/CEEM.2012.6410575
- Ezzat MA, El-Karamany AS. Magnetothermoelasticity with two relaxation times in conducting medium with variable electrical and thermal conductivity. Appl. Math. Comput. 2003;142:449–467.
- Ezzat MA, El-Bary AA. State space approach of two-temperature magneto-thermoelasticity with thermal relaxation in a medium of perfect conductivity. Int. J. Eng. Sci. 2009;47:618–630.10.1016/j.ijengsci.2008.12.012
- Abel NH. Solutions de quelques problèmes à l’aide d’intégrales defines. Oeuvres complètes. nouvelle éd. Vol. 1. Christiania: Grondahl & Son; 1881. p. 11–27. Edition de Holmboe; 1926.
- Oldham KB, Spanier J. The fractional calculus. New York (NY): Academic Press; 1974.
- Gorenflo R, Mainardi F. Fractional calculus: Integral and differential equations of fractional orders, fractals and fractional calculus in continuum mechanics. Wien: Springer; 1997.
- Hilfer R. Applications of fraction calculus in physics. Singapore: World Scientific; 2000.
- Caputo M. Vibrations on an infinite viscoelastic layer with a dissipative Memory. J. Acoust. Soc. Am. 1974;56:897–904.10.1121/1.1903344
- Ezzat MA, El-Karamany AS, El-Bary AA, Fayik M. Fractional ultrafast laser-induced magneto-thermoelastic behavior in perfect conducting metal films. J Electromag. Waves Applics. 2014;28:64–82.10.1080/09205071.2013.855616
- Podlubny I. Fractional differential equations. New York (NY): Academic Press; 1999.
- Ezzat MA. Thermoelectric MHD non-Newtonian fluid with fractional derivative heat transfer. Phys. B. 2010;405:4188–4194.10.1016/j.physb.2010.07.009
- Jumarie G. Derivation and solutions of some fractional Black_Scholes equations in coarse-grained space and time. Application to Mferton’s optimal portfolio. Comput. Math. Appli. 2010;59:1142–1164.10.1016/j.camwa.2009.05.015
- El-Karamany AS, Ezzat MA. On the two-temperature Green-Naghdi thermoelasticity theories. J. Thermal Stress. 2011;34:264–284.10.1080/01495739.2010.545741
- El-Karamany AS, Ezzat MA. On fractional thermoelasticity. Math. Mech. Solid. 2011;16:334–346.
- Ezzat MA, El-Karamany AS. Fractional order theory of a perfect conducting thermoelastic medium. Can. J. Phys. 2011;89:311–318.10.1139/P11-022
- Povstenko YZ. Fractional heat conductive and associated thermal stress. J. Therm. Stress. 2004;28:83–102.10.1080/014957390523741
- Youssef HM. Theory of fractional order generalized thermoelasticity. J. Heat Transfer. 2010;132:1–7.
- Ezzat MA, El-Karamany AS. State space approach of two-temperature magneto-viscoelasticity theory with thermal relaxation in a medium of perfect conductivity. J. Therm. Stress. 2009;32:819–838.10.1080/01495730802637225
- Ezzat MA, El-Bary AA, El-Karamany AS. Two-temperature theory in generalized magneto-thermo-viscoelasticity. Can. J. Phys. 2009;87:329–336.10.1139/P08-143
- Sherief HH, El-Sayed A, Abd El-Latief A. Fractional order theory of thermoelasticity. Int. J. Solid Struct. 2010;47:269–275.10.1016/j.ijsolstr.2009.09.034
- Ezzat MA. Free convection effects on perfectly conducting fluid. Int. J. Eng. Sci. 2001;39:799–819.10.1016/S0020-7225(00)00059-8
- Ichkawa S, Kishima A. Application of Fourier series technique to inverse Laplace transform. Kyoto University, Japan. 1972;34:53–67.
- Honig G, Hirdes U. A method for the numerical inversion of the Laplace transform. J. Comp Appl Math. 1984;10:113–132.10.1016/0377-0427(84)90075-X
- Ezzat MA, El-Karamany AS. Fractional thermoelectric viscoelastic materials. J. Appl. Poly. Sci. 2012;124:2187–2199.10.1002/app.v124.3
- Povstenko YZ. Fractional heat conduction and associated thermal stress. J. Thermal Stress. 2005;28:83–102.
- Ezzat MA. Magneto-thermoelasticity with thermoelectric properties and fractional derivative heat transfer. Phys. B. 2011;406:30–35.