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This work deals with the study of transient responses in a two-temperature generalized thermoelastic infinite medium having a cylindrical cavity due to a time-dependent moving heat source where the conventional Fourier's law of heat conduction is modified by introducing a new Taylor's series expansion using memory-dependent derivative (MDD). The resulting non-dimensional equations are applied to a specific problem. A direct approach is introduced to obtain the analytical expressions of the physical quantities in the Laplace transform domain. The inversion of the Laplace transforms are carried out using the methods based on the Fourier series expansion technique. Numerical results for the dynamical and conductive temperatures, stress, strain, and displacement are presented graphically. The effects of time-delay and kernel function have been studied on the thermo-physical quantities. K E Y W O R D S kernel function, Laplace transform, memory-dependent derivative, moving heat source, time-delay, twotemperature with ( − ) = ( − ) − −1 Γ( − ) , where ( ) indicates the usual -th order derivative of the function.