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International Journal of ADVANCED AND APPLIED SCIENCES Int. j. adv. appl. sci. 2313626X 23133724 7 2022 7 2022 9 7 Magneto-thermoelasticity Greenâ€“Naghdi theory with memory-dependent derivative in the presence of a moving heat source Department of Mathematics, Faculty of Science, Northern Border University, Arar, Saudi Arabia El-Attar et al. In the present work, a mathematical model of the Green-Naghdi thermoelasticity theory of type III (GN-III) with memory-dependent derivative (MDD) heat transfer for a perfectly conducting isotropic media has been constructed. The state-space and Laplace transform techniques are adopted for the solution of a half-space problem in the presence of a moving heat source with constant velocity. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results for all fields are given and illustrated graphically. Comparison is made with the results predicted by coupled thermoelasticity (DCT). The influences of MDD parameters and heat source speed on all fields are examined. 7 2022 7 2022 33 41 10.21833/ijaas-crossmark www.science-gate.com true IASE www.science-gate.com 10.21833/ijaas.2022.07.005 http://www.science-gate.com/IJAAS/2022/V9I7/1021833ijaas202207005.html - http://science-gate.com/IJAAS/Articles/2022/2022-9-7/1021833ijaas202207005.pdf