Numerical Simulation of Generalized Fractional Thermoelasticity With Two Temperature and Phase Lags in a Half Space Using GLA‐PINN

This research manuscript presents a model of heat conduction incorporating two‐phase lags and time fractional derivatives to precisely identify the nonsimple behaviors of thermoelastic materials. Generalized fractional differentiation operators with nonsingular kernels are considered. The model incorporates the two‐temperature idea and a two‐stage delay technique to account for microstructure effects. Thermoelastic relationships between isotropic substances and the exterior body forces were investigated as a real‐world application of the new idea. There is some analysis of the impact of the fractional differential operators. Furthermore, an innovative physics‐informed neural network (PINN) technique named GLA‐PINN has been developed to investigate the behavior of the fractional thermoelasticity model. The system of fractional partial differential equations is solved through the proposed novel technique. The graphical representations generated by computational outputs were utilized to illustrate the researched physical fields’ behavior. The residual error graphs and the loss graphs indicate the validation and accuracy of the developed technique. The extended model of fractional heat conduction is shown to be suitable for giving temperature forecasting. The results concluded that the suggested framework could be beneficial in solving problems in anomalous transport, heat conduction, and analysis of the other branches of engineering.