Impact of Memory-dependent Response of a Thermoelastic Thick Solid Cylinder

[1] Oldham, K.B., Spanier, J., The Fractional Calculus, Academic Press, New York, 1974.

[2] Samko, S.G., Kilbas, A.A., Marichev, O.I., Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Amsterdam, 1993.

[3] Miller, K.S., Ross, B., An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley–Blackwell, New York, 1993.

[4] Podlubny, I., Fractional Differential Equations, Academic Press, San Diego, 1999.

[5] Diethelm, K., The Analysis of Fractional Differential Equations, Springer, Berlin, 2010.

[6] Kilbas, A.A., Srivastava, H.M., Trujillo, J.J., Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.

[7] Povstenko, Y.Z., Fractional heat conduction equation and associated thermal stresses, Journal of Thermal Stresses, 28(1), 2005, 83–102.

[8] Povstenko, Y.Z., Two-dimensional axisymmetric stresses exerted by instantaneous pulses and sources of diffusion in an infinite space in a case of time-fractional diffusion equation, International Journal of Solids and Structures, 44(7–8), 2007, 2324–2348.

[9] Povstenko, Y.Z., Thermoelasticity which uses fractional heat conduction equation, Mathematical Methods and Physicomechanical Fields, 51(2), 2008, 239–246.

[10] Povstenko, Y.Z., Fractional radial diffusion in a cylinder, Journal of Molecular Liquids, 137(1–3), 2008, 46–50.

[11] Povstenko, Y.Z., Thermoelasticity which uses fractional heat conduction equation, Journal of Mathematical Sciences, 162, 2009, 296–305.

[12] Povstenko, Y.Z., Theory of thermoelasticity based on the space-time-fractional heat conduction equation, Physica Scripta, 136, 2009, 014017-1-6.

[13] Lamba, N.K., Thermosensitive response of a functionally graded cylinder with fractional order derivative, International Journal of Applied Mechanics and Engineering, 27(1), 2022, 107-124.

[14] Lamba, N.K., Deshmukh, K.C., Hygrothermoelastic response of a finite solid circular cylinder, Multidiscipline Modeling in Materials and Structures, 16(1), 2020, 37-52.

[15] Lamba, N.K., Deshmukh, K.C., Hygrothermoelastic response of a finite hollow circular cylinder, Waves in Random and Complex Media, 2022, doi: 10.1080/17455030.2022.2030501.

[16] Thakare, S., Warbhe, M.S., Lamba, N.K., Time fractional heat transfer analysis in nonhomogeneous thick hollow cylinder with internal heat generation and its thermal stresses, International Journal of Thermodynamics, 23(4), 2020, 281-302.

[17] Wang J.L., Li, H.F., Surpassing the fractional derivative: Concept of the memory-dependent derivative, Computers and Mathematics with Applications, 62, 2011, 1562–1567.

[18] Ahmed, S.K., Ezzat, M.A., Modified Fourier's Law with Time-Delay and Kernel Function: Application in Thermoelasticity, Journal of Thermal Stresses, 38(7), 2015, 811-834.

[19] Sun, W.W., Wang, J.L., Reconstruct the Heat Conduction Model with Memory Dependent Derivative, Applied Mathematics, 9, 2018, 1072-1080.

[20] Xue, Z.N., Chen, Z.T., Tian, X.G., Transient thermal stress analysis for a circumferentially cracked hollow cylinder based on memory-dependent heat conduction model, Theoretical and Applied Fracture Mechanics, 96, 2018, 123–133.

[21] Ma, Y., Gao, Y., Dynamic response of a hollow cylinder subjected to thermal shock considering scale effect and memory dependent effect, Mechanics of Advanced Materials and Structures, 29(25), 2022, 4468-4477.

[22] Marchi, E., Fasulo, A., Heat conduction in sector of hollow cylinder with radiation, Atti della Reale Accademia delle scienze di Torino, 1, 1967, 373-382.

[23] Ozisik, M.N., Boundary Value Problems of Heat Conductions, International text book Company, Scranton, Pennsylvania, 1986.

[24] Noda, N., Hetnarski, R.B., Tanigawa, Y., Thermal stresses, Second ed., Taylor and Francis, New York, 2003.

[25] Kumar, R., Lamba N.K., Varghese, V., Analysis of thermoelastic disc with radiation conditions on the curved surfaces, Materials Physics and Mechanics, 16, 2013, 175-186.

[26] Marin M., Contributions on uniqueness in thermoelastodynamics on bodies with voids, Ciencias Matematicas (Havana), 16(2), 1998, 101-109.

[27] Marin M., A temporally evolutionary equation in elasticity of micropolar bodies with voids, UPB Scientific Bulletin, Series A: Applied Mathematics Physics, 60(3-4), 1998, 3-12.

[28] Kamdi, D., Lamba, N.K., Thermoelastic Analysis of Functionally Graded Hollow Cylinder Subjected to Uniform Temperature Field, Journal of Applied and Computational Mechanics, 2(2), 2016, 118-127.

[29] Manthena, V.R., Lamba, N.K., Kedar, G.D., Springbackward Phenomenon of a Transversely Isotropic Functionally Graded Composite Cylindrical Shell, Journal of Applied and Computational Mechanics, 2(3), 2016, 134-143.

[30] Varghese, V., An Analysis of Thermal-Bending Stresses in a Simply Supported Thin Elliptical Plate, Journal of Applied and Computational Mechanics, 4(4), 2018, 299-309.

[31] Abouelregal, A.E., Moustapha, M.V., Nofal, T.A., Rashid, S., Ahmad, H., Generalized thermoelasticity based on higher-order memory-dependent derivative with time delay, Results in Physics, 20, 2021, 103705.

[32] Abouelregal, A.E., Sedighi, H.M., Faghidian, S.A., Shirazi, A.H., Temperature-dependent physical characteristics of the rotating nonlocal nanobeams subject to a varying heat source and a dynamic load, Facta Universitatis, Series: Mechanical Engineering, 19(4), 2021, 633-656.

[33] Abouelregal, A.E., Atta, D., Sedighi, H.M., Vibrational behavior of thermoelastic rotating nanobeams with variable thermal properties based on memory-dependent derivative of heat conduction model, Archive of Applied Mechanics, 93, 2023, 197–220.

[34] Abouelregal, A.E., Askar, S.S., Marin, M., Badahiould M., The theory of thermoelasticity with a memory-dependent dynamic response for a thermo-piezoelectric functionally graded rotating rod, Scientific Reports, 13, 2023, 9052.

[35] Atta, D., Thermal Diffusion Responses in an Infinite Medium with a ‎Spherical Cavity using the Atangana-Baleanu Fractional ‎Operator, Journal of Applied and Computational Mechanics, 8(4), 2022, 1358-1369.