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The influence of the temperature discrepancy parameter and higher order of the time-derivative is discussed. Classical coupled and generalized hygrothermoelasticity models are recovered by considering the various special cases and illustrated graphically.

The theory of integral transformations has been used to study a new hygrothermal model that includes higher-order time derivatives with three-phase-lags and memory-dependent derivatives (MDD). This model considers the microscopic structure’s influence on a non-simple hygrothermoelastic infinitely long cylinder. The generalized Fourier and Fick’s law was adopted to derive the linearly coupled partial differential equations with higher-order time-differential with the two-phase lag model, including memory-dependent derivatives for the hygrothermal field. The investigation of microstructural interactions and the subsequent hygrothermal change has been undertaken as a result of the delay time and relaxation time translations.

These two-phase-lag models are also practically applicable in modeling nanoscale heat and moisture transport problems applied to almost all important devices. This work will enable future investigators to gain insight into non-simple hygrothermoelasticity with different phase delays of higher order in detail.

To the best of my knowledge, and after completing an intensive search of the relevant literature, the author could not learn any published research that presents a general solution for a higher-order time-fractional three-phase-lag hygrothermoelastic infinite circular cylinder with memory memory-dependent derivative.