[1] A. Bayat, H. Moosavi and Y. Bayat, Thermo-mechanical analysis of functionally graded thick spheres with linearly time dependent temperature, Sci. Iran. B. 22 (2015), 1801—1812.
[2] N.M. Dien, Nonlinear sequential fractional boundary value problems involving generalized ψ-Caputo fractional derivatives, Filomat, 36 (2022), no. 15, 5047–5058.
[3] M.A. Ezzat, A. Karamany and A.A. El-Bary, Application of fractional order theory of thermoelasticity to 3D time dependent thermal shock problem for a half-space, Mech. Adv. Materials Struc. 226 (2016), 27—35.
[4] K.R. Gaikwad, Analysis of thermoelastic deformation of a thin hollow circular disk due to partially distributed heat supply, J. Thermal Stresses 36 (2013), 207–224.
[5] K.R. Gaikwad, Mathematical modelling of thermoelastic problem in a circular sector disk subject to heat generation, Int. J. Adv. Appl. Math. Mech. 2 (2015), 183–195.
[6] K.R. Gaikwad, Two-dimensional steady-state temperature distribution of a thin circular plate due to uniform internal energy generation, Cogent Math. 3 (2016), 1–10.
[7] K.R. Gaikwad and K.P. Ghadle, Nonhomogeneous heat conduction problem and its thermal deflection due to internal heat generation in a thin hollow circular disk, J. Thermal Stresses 35 (2012), 485–498.
[8] K.R. Gaikwad and K.P. Ghadle, On a certain thermoelastic problem of temperature and thermal stresses in a thick circular plate, Aust. J. Basic Appl. Sci. 6 (2012), 34–48.
[9] K.R. Gaikwad and S.G. Khavale, Time fractional heat conduction problem in a thin hollow circular disk and it’s thermal deflection, Easy Chair 1672 (2019), 1–11.
[10] K.R. Gaikwad and S.G. Khavale, Time fractional 2D thermoelastic problem of thin hollow circular disk and it’s associated thermal stresses, Bull. Marathwada Math. Soc. 21 (2020), no. 1-2, 37-–47.
[11] K.R. Gaikwad and S.G. Khavale, Fractional order transient thermoelastic stress analysis of a thin circular sector disk, Int. J. Thermodyn. 25 (2022), no. 1, 1-–8.
[12] K.R. Gaikwad and Y.U. Naner, Analysis of transient thermoelastic temperture distribution of a thin circular plate and its thermal deflection under uniform heat generation, J. Thermal Stress 44 (2021), no. 1, 75–85.
[13] K.R. Gaikwad, Y.U. Naner and S.G. Khavale, Time fraectional thermoelastic stress anlysis of a thin rectangular plate, NOVYI MIR Res. J. 6 (2021), no. 1, 42–56.
[14] K.R. Gaikwad, Y.U. Naner and S.G. Khavale, Transient thermoelastic bending analysis of a rectangular plate with a simply supported edge under heat source: Green’s function approach, Int. J. Nonlinear Anal. Appl. 14 (2022), no. 1, 805—818.
[15] E.M. Hussain, Fractional order thermoelastic problem for an infinitely long solid circular cylinder, J. Thermal Stresses 38 (2014), 133—145.
[16] A. Kar and M. Kanoria, Generalized thermoelasticity problem of a hollow sphere under thermal shock, Eur. J. Pure Appl. Math. 2 (2009), 125—146.
[17] S.G. Khavale and K.R. Gaikwad, Generalized theory of magneto-thermo-viscoelastic Spherical cavity problem under Fractional order derivative: State Space Approach, Adv. Math.: Sci. J. 9 (2020), 9769–9780.
[18] S.G. Khavale and K.R. Gaikwad, Fractional order thermoelatic problem of thin hollow circular disk and its thermal stresses under axi-symmetric heat supply, Design Engin. 2021 (2021), no. 9, 13851–13862.
[19] S.G. Khavale and K.R. Gaikwad, 2D problem for a sphere in the fractional order theory thermoelasticity to axisymmetric temperature distribution, Adv. Math.: Sci. J. 11 (2022), no. 1, 1–15.
[20] S.G. Khavale and K.R. Gaikwad, Analysis of non-integer order thermoelastic temperature distribution and thermal deflection of thin hollow circular disk under the axi-symmetric heat supply, J. Korean Soc. Ind. Apll. Math. 26 (2022), no. 1, 67-–75.
[21] S.G. Khavale and K.R. Gaikwad, Two-dimensional generalized magneto-thermo-viscoelasticity problem for a spherical cavity with one relaxation time using fractional derivative, Int. J. Thermodyn. 25 (2022), no. 2, 89—97.
[22] B.G. Korenev, Bessel Functions and Their Applications. Boca Raton: CRC Press, 2003.
[23] S. Mukhopadhay and R. Kumar, A study of generalized thermoelastic interactions in an unbounded medium with a spherical cavity, Comput. Math. Appl. 56 (2008), 2329—2339.
[24] N.M. Ozisik, Boundary Value Problem Of Heat Conduction, International Textbook Company, Scranton, Pennsylvania, 1968.
[25] I. Podlubny, Fractional differential Equation, Academic Press, San Diego, 1999.
[26] Y.Z. Povstenko, Fractional heat conduction equation and associated thermal stresses, J. Thermal Stresses 28 (2005), 83–102.
[27] Y.Z. Povstenko, Thermoelasticity that uses fractional heat conduction equation, J. Math. Science, 162 (2009), 296–305.
[28] Y.Z. Povstenko, Fractional Thermoelasticity, Springer, New York, 2015.
[29] PTC Mathcad Prime-7.0.0.0, [Online]. Available: https://support.ptc.com/help/mathcad/r7.0/en/ (accessed Dec. 1, 2021).
[30] W. Raslan, Application of fractional order theory of thermoelasticity to a 1D problem for a cylindrical cavity, Arch. Mech. 66 (2014), 257–267.
[31] W. Raslan, Application of fractional order theory of thermoelasticity in a thick plate under axisymmetric temperature distribution, J. Thermal Stresses 38 (2015), 733–743.
[32] M.A. Ragusa and A. Razani, Existence of a periodic solution for a coupled system of differential equations, AIP Conf. Proc. 2425 (2022), Article ID 370004.
[33] A. Selvam, S. Sabarinathan, S. Noeiaghdam and V. Govindan, Fractional Fourier transform and Ulam stability of fractional differential equation with fractional Caputo type derivative, J. Funct. Spaces 2022 (2022), Article ID 3777566.
[34] H.H. Sherief, A. El-Said and A. Abd El-Latief, Fractional order theory of thermoelasticity, Int.J. Solids Struct. 47 (2010) 269–275.
[35] I.N. Sneddon, The use of Integral Transform, McGraw Hill, New York, 1972.
[36] A. Sur and M. Kanoria, Fractional order two-temperature thermoelasticity with wave speed, Acta Mech. 223 (2012) 2685–2701.
[37] A. Sur and M. Kanoria, Fractional order generalized thermoelastic functionally graded solid with variable material properties, J. Solid Mech. 6 (2014), 54–69.
[38] J.J. Tripathi, G.D. Kedar and K.C. Deshmukh, Generalized thermoelastic diffusion problem in a thick circular plate with axisymmetric heat supply, Acta Mech. 226 (2015), 2121–2134.
[39] H.M. Youssef, Two-dimensional thermal shock problem of fractional order generalized thermoelasticity, Acta Mech. 223 (2012), 1219–1231.