The present work is devoted to the derivation of fundamental equations in
generalized thermoelastic diffusion with four lags and higher-order
time-fractional derivatives. The equations of the heat conduction and the
mass diffusion have been modified by using Taylor’s series of time-fractional order. In this new model, the Fourier and the Fick laws have been
modified to include a higher time-fractional order of the heat conduction
vector, the gradient of temperature, the diffusing mass flux and the
gradient of chemical potential. We adopted the definitions of Caputo and
Jumarie; for time-fractional derivatives. The work of Nowacki; Sherief,
Hamza, and Saleh; and Aouadi; are deduced as limit cases from the current
investigation. Applying this formulation, we have discussed a thermoelasticdiffusion problem for a half-space exposed to thermal and chemical shock
with a permeable material in contact with the half-surface. We discussed
the sensitivity of the different physical parameters in all studied fields in
detail and the results are presented graphically as well as in tabular forms.