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Original Article

Magneto-thermoelasticity with two fractional order heat transferFootnote

, &
Pages 70-79 | Received 25 Feb 2014, Accepted 19 Jun 2014, Published online: 27 Mar 2018

References

  • M.BiotThermoelasticity and irreversible thermodynamicsJ. Appl. Phys.271956240253
  • M.CaputoLinear models of dissipation whose Q is almost frequency independent IIGeophys. J. Roy. Astron. Soc.31967529539
  • M.CaputoF.MainardiLinear model of dissipation in anelastic solidsRivis ta el Nuovo cimento11971161198
  • M.CaputoVibrations on an infinite viscoelastic layer with a dissipative memoryJ. Acoust. Soc. Am.561974897904
  • C.CattaneoSur une forme de l’e’quation de la Chaleur e’liminant le paradoxe d’une propagation instantane’eComptes Rendus Academic des Sciences2471958431433
  • D.S.ChandrasekharaiahA temperature-rate dependent thermo-piezoelectricityJ. Therm. Stresses71984293306
  • P.J.ChenM.E.GurtinOn a theory of heat conduction involving two temperaturesZAMP191968614627
  • P.J.ChenM.E.GurtinW.O.WilliamsA note on non-simple heat conductionZAMP191968969970
  • P.J.ChenM.E.GurtinW.O.WilliamsOn the thermodynamics of non-simple elastic materials with two temperaturesZAMP201969107112
  • A.S.El-KaramanyM.A.EzzatConvolutional variational principle, reciprocal and uniqueness theorems in linear fractional two-temperature thermoelasticityJ. Therm. Stresses342011264284
  • M.A.EzzatA.A.El-BaryA.S.El-KaramanyTwo-temperature theory in generalized magneto-thermo-viscoelasticityCan. J. Phys.872009329336
  • M.A.EzzatA.S.El-KaramanyThe uniqueness and reciprocity theorems for generalized thermoviscoelasticity for anisotropic mediaJ. Therm. Stresses252002507522
  • M.A.EzzatFree convection effects on perfectly conducting fluidInt. J. Eng. Sci.392001699819
  • M.A.EzzatFundamental solution in generalized magneto-thermoelasticity with two relaxation times for perfect conductor cylindrical regionInt. J. Eng. Sci.4200415031519
  • M.A.EzzatState space approach to solids and fluidsCan. J. Phys.86200812411250
  • M.A.EzzatMagneto-thermoelasticity with thermoelectric properties and fractional derivative heat transferPhysica B40620113035
  • M.A.EzzatA.S.El-KaramanyFractional order theory of a perfect conducting thermoelastic mediumCan. J. Phys.892011311318
  • R.GorenfloF.MainardiFractional Calculus: Integral and Differential Equations of Fractional Orders, Fractals and Fractional Calculus in Continuum Mechanics1997SpringerWien
  • R.HilferApplications of Fraction Calculus in Physics2000World ScientificSingapore
  • G.HonigU.HirdesA method for the numerical inversion of the Laplace transformJ. Comput. Appl. Math.101984113132
  • D.IeşanOn the linear coupled thermoelasticity with two temperaturesZAMP211970583591
  • J.IgnaczakUniqueness in generalized thermoelasticityJ. Therm. Stresses21979171175
  • J.IgnaczakM.Ostoja-starzeweskiThermoelasticity with finite wave speeds2009Oxford University PressNew York
  • B.B.JaiminiN.ShrivastavaH.M.SrivastavaThe integral analogue of the Leibniz rule for fractional calculus and its applications involving functions of several variablesComput. Math. Appl.412001149155
  • D.JosephL.PreziosiHeat WavesRev. Modern Phys.621990375391
  • G.JumarieDerivation and solutions of some fractional Black–Scholes equations in coarse-grained space and time. Application to Mferton’s optimal portfolioComput. Math. Appl.59201011421164
  • S.KaliskiJ.PetykiewiczEquation of motion coupled with the field of temperature in a magnetic field involving mechanical and electrical relaxation for anisotropic bodiesProc. Vibr. Probl.41959112
  • V.KiryakovaGeneralized fractional calculus and applicationsPitman Research Notes in Mathematics Seriesvol. 3011994Longman-WileyNew York
  • H.LordY.ShulmanA generalized dynamical theory of thermo-elasticityJ. Mech. Solids Phys.151967299309
  • A.MagañaR.QuintanillaUniqueness and growth of solutions in two-temperature generalized thermoelastic theoriesMath. Mech. Solids142009622634
  • F.MainardiFractional calculus: some basic problems in continuum and Statistical mechanics’A.CarpinteriF.MainardiFractals and Fractional Calculus in Continuum Mechanics1997Springer-VerlagNew York291348
  • K.S.MillerB.RossAn Introduction to the Fractional Integrals and Derivatives – Theory and Applications1993John Wiley and Sons IncNew York
  • I.PodlubnyFractional Differential Equations1999Academic PressNew York
  • Y.PovstenkoFractional heat conductive and associated thermal stressJ. Therm. Stresses28200483102
  • Y.Z.PovstenkoFractional heat conduction equation and associated thermal streesesJ. Therm. Stresses28200583102
  • P.PuriP.M.JordanOn the propagation of harmonic plane waves under the two-temperature theoryInt. J. Eng. Sci.44200611131126
  • Y.A.RossikhinM.V.ShitikovaApplications of fractional calculus to dynamic problems of linear and nonlinear heredity mechanics of solidsAppl. Mech. Rev.5019971567
  • H.SheriefOn uniqueness and stability in generalized thermoelasticityQ. J. Appl. Math.451987773778
  • H.H.SheriefA.El-SaidA.Abd El-LatiefFractional order theory of thermoelasticityInt. J. Solid Struct.472010269275
  • H.YoussefTheory of two-temperature generalized thermoelasticityIMA J. Appl. Math.712006383390
  • H.YoussefTheory of fractional order generalized thermoelasticityJ. Heat Transf.132201017

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