Sự tương tác cơ- nhiệt trong một chất rắn nhiệt đàn hồi tổng quát bậc phân số với sự khuếch tán

Biot M (1956) Thermoelasticity and irreversible thermo-dynamics. J Appl Phys 27:240–253 Caputo M (1967) Linear model of dissipation whose Q is almost frequency independent-II. Geophys J R Astro Soc 13:529–539 Chandrasekharaiah DS (1998) Hyperbolic thermoelasticity: a review of recent literature. Appl Mech Rev 51:705–729 Danilovskaya V (1950) Thermal stresses in an elastic half-space due to sudden heating of its boundary. Prikl Mat Mekh 14:316–318 Deswal S, Choudhary S (2008) Two dimensional interactions due to moving load in generalized thermoelastic solid with diffusion. Appl Math Mech 29:207–221 Deswal S, Kalkal K (2011) A two-dimensional generalized electro-magneto-thermo-viscoelastic problem for a half-space with diffusion. Int J Therm Sci 50:749–759 Deswal S, Kalkal K (2014) Plane waves in a fractional order micropolar magneto-thermoelastic half-space. Wave Motion 51:100–113 Dhaliwal R, Sherief H (1980) Generalized thermoelasticity for anisotropic media. Quart Appl Math 33:1–8 Ezzat MA (2010) Thermoelectric MHD non-Newtonian fluid with fractional derivative heat transfer. Phys B 405:4188–4194 Ezzat MA (2011) Magneto-thermoelasticity with thermoelectric properties and fractional derivative heat transfer. Phys B 406:30–35 Ezzat MA, El-Bary AA (2016a) Generalized fractional magneto-thermo-viscoelasticity. Microsyst Technol. doi:10.1007/s00542-016-2904-5 Ezzat MA, El-Bary AA (2016b) Application of fractional order theory of magneto-thermoelasticity to an infinite perfect conducting body with a cylindrical cavity. Technol, Microsyst. doi:10.1007/s00542-016-2976-2 Ezzat MA, Fayik MA (2011) Fractional order theory of thermoelastic diffusion. J Therm Stresses 34:851–872 Green AE, Lindsay KA (1972) Thermoelasticity. J Elast 2:1–7 Green AE, Naghdi PM (1991) A re-examination of the basic postulates of thermo-mechanics. Proc R Soc Lond A 432:171–194 Green AE, Naghdi PM (1992) On undamped heat waves in an elastic solid. J Therm Stresses 15:253–264 Green AE, Naghdi PM (1993) Thermoelasticity without energy dissipation. J Elast 31:189–209 Hetnarski RB, Ignaczak J (1999) Generalized thermoelasticity. J Therm Stresses 22:451–476 Jumarie G (2010) Derivation and solutions of some fractional Black- Scholes equations in coarse-grained space and time. Application to Merton’s optimal portfolio. Comp Math Appl 59:1142–1164 Kalkal KK, Deswal S (2014) Generation of magneto-thermodiffusive plane waves in solids due to mechanical load. Int J Comput Methods Eng Sci Mech 15:322–329 Kumar S, Sikka JS, Choudhary S (2016) Three-dimensional analysis of a thermo-viscoelastic half-space due to thermal shock in temperature-rate-dependent thermoelasticity. J Mech 32:401–411 Lord HW, Shulman Y (1967) A generalized dynamical theory of thermoelasticity. J Mech Phys Solids 15:299–309 Miller KS, Ross B (1993) An Introduction to the fractional calculus and fractional differential equation. John Wiley and Sons, New York Nowacki W (1974a) Dynamical problems of thermodiffusion in solids I. Bull Acad Pol SciSer Sci Tech 22:55–64 Nowacki W (1974b) Dynamical problems of thermodiffusion in solids II. Bull Acad Pol SciSer Sci Tech 22:129–135 Nowacki W (1974c) Dynamical problems of thermodiffusion in solids III. Bull Acad Pol SciSer Sci Tech 22:257–266 Nowacki W (1976) Dynamic problems of diffusion in solids. Eng Fract Mech 8:261–266 Olesiak ZS, Pyryev YA (1995) A coupled quasi-stationary problem of thermodiffusion for an elastic cylinder. Int J Eng Sci 33:773–780 Podlubny I (1999) Fractional differential equations. Academic Press, New York Podstrigach Ya S (1961) Differential equations of the problem of thermodiffusion in a solid deformable isotropic body. Dop Akad Nauk Ukr RSR No 2:169–172 Podstrigach Ya S (1964) The diffusion theory of strain of an isotropic solid medium. Vopr Mekh Real Tver Tela No 2:71–99 Povstenko YZ (2005) Fractional heat conduction equation and associated thermal stress. J Therm Stresses 28:83–102 Povstenko YZ (2011) Fractional Cattaneo-type equations and generalized thermoelasticity. J Therm Stresses 34:97–114 Povstenko YZ (2015) Fractional Thermoelasticity. Springer, New York Ross B (1977) The development of fractional calculus. Hist Math 4:75–89 Sharma JN, Kumar V (1997) Plane strain problems of transversely isotropic thermoelastic media. J Therm Stresses 20:463–476 Sharma N, Kumar R, Ram P (2008) Plane strain deformation in generalized thermoelastic diffusion. Int J Thermophys 29:1503–1522 Sheoran SS, Kalkal KK, Deswal S (2016) Fractional order thermo-viscoelastic problem with temperature dependent modulus of elasticity. Mech Adv Mater Struct 23:407–414 Sherief H, Saleh H (2005) A half-space problem in the theory of generalized thermoelastic diffusion. Int J Solids Struct 42:4484–4493 Sherief H, Hamza F, Saleh H (2004) The theory of generalized thermoelastic diffusion. Int J Eng Sci 42:591–608 Sherief H, El-Sayed AM, El-Latief AA (2010) Fractional order theory of thermoelasticity. Int J Solids Struct 47:269–275 Yadav R, Kalkal KK, Deswal S (2015) Two-temperature generalized thermoviscoelasticity with fractional order strain subjected to moving heat source: State space approach. J Math 2015:1–13 (Article ID 487513 ) Youssef HM (2010) Theory of fractional order generalized thermoelasticity. ASME J Heat Transf 132:1–7