A novel model with theoretical investigations of generalized hyperbolic two-temperature theory in the context of the generalized thermoelasticity theory is studied. The elastic medium is excited at the outer surface by an external magnetic field and pulsed laser. The model is established in the context of the memory-depended derivative (MDD) when the elastic material time-dependent. The governing equations describe the interaction processes for isotropic homogeneous hyperbolic thermoelastic elastic medium in onedimensional (1D) deformation when the non-Gaussian laser pulse model is applied with time delay. The Laplace transform is used to obtain the analytical solutions of the main physical fields. The medium is loaded when a traction is free and thermally shocked with time-dependent. The complete solutions are obtained in the Laplace time domain when used the inverse of Laplace transform numerically. Numerical results of the main physical quantities are discussed graphically under the effect of hyperbolic two-temperature, magnetic field and laser pulses when the time-delay parameter is taken into consideration.