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In this work, the fractional order theory of thermoelasticity is introduced to study a two-dimensional fiber-reinforced problem in a half-space. The governing equations are formulated by considering the effect of the magnetic field, gravity, and moving heat source on a fiber-reinforced linearly thermoelastic isotropic medium. These equations are then transformed into non-dimensional forms. The normal mode analysis is used to solve this problem to obtain the exact expressions of the non-dimensional temperature, displacement components, and stress. The distributions of these considered variables are obtained and illustrated graphically. Comparisons are taken with the results in the presence and absence of the magnetic field, gravity and heat source under the fractional order theory of thermoelasticity. The results show that the existence of the magnetic field, gravity, and heat source have significant influence on the distributions of the considered variables.

Effect of magnetic field and gravity on 2D fiber-reinforced medium under fractional order theory of thermoelasticity