Islamic Azad University - Arak BranchJournal of Solid Mechanics2008-35056120140330Fractional Order Generalized Thermoelastic Functionally Graded Solid with Variable Material Properties5469514587ENASurDepartment of Applied Mathematics, University of CalcuttaMKanoriaDepartment of Applied Mathematics, University of CalcuttaJournal Article20130923In this work, a new mathematical model of thermoelasticity theory has been considered in the context of a new consideration of heat conduction with fractional order theory. A functionally graded isotropic unbounded medium is considered subjected to a periodically varying heat source in the context of space-time non-local generalization of three-phase-lag thermoelastic model and Green-Naghdi models, in which the thermophysical properties are temperature dependent. The governing equations are expressed in Laplace-Fourier double transform domain and solved in that domain. Then the inversion of the Fourier transform is carried out by using residual calculus, where poles of the integrand are obtained numerically in complex domain by using Laguerreâ€™s method and the inversion of Laplace transform is done numerically using a method based on Fourier series expansion technique. The numerical estimates of the thermal displacement, temperature and thermal stress are obtained for a hypothetical material. Finally, the obtained results are presented graphically to show the effect of non-local fractional parameter on thermal displacement, temperature and thermal stress. A comparison of the results for different theories (three-phase-lag model, GN model II, GN model III) is presented and the effect of non-homogeneity is also shown. The results, corresponding to the cases, when the material properties are temperature independent, agree with the results of the existing literature.http://jsm.iau-arak.ac.ir/article_514587_c72f2f23176c6c2e92000d63adb4eacb.pdf