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The present research work is focused on mathematical model for the study of variations of fractional order strain (FoS) in transversely isotropic homogeneous thick circular plate with hyperbolic two temperature (H2T), ring load, with & without energy dissipation. The Laplace and Hankel transform has been used for finding the general solution to the field equations. The analytical expressions of displacement components, conductive temperature and stress components are computed in the transformed domain. Numerical inversion techniques have been applied to obtain the solution in physical domain. Comparisons are made for Classical two temperature with fractional order strain and hyperbolic two temperature with fractional order strain and depicted graphically using the MATLAB software. Some particular cases are also figured out from the present investigation.