Thepresentworkaimstoestablishafractional-ordergeneralizedthemoelasticdiffusiontheoryforanisotropicandlinearlythermoelasticdiffusivemedia.Tonumericallyhandlethemulti-physicsproblemsexpressedbyasequenceofincompletedifferentialequations,particularlybyafractionalequation,ageneralizedvariationalprincipleisobtainedfortheunifiedtheoryusingasemi-inversemethod.Innumericalimplementation,thedynamicresponseofasemi-infinitemediumwithoneendsubjectedtoathermalshockandachemicalpotentialshockisinvestigatedusingtheLaplacetransform.Numericalresults,i.e.,non-dimensionaltemperature,chemicalpotential,anddisplacement,arepresentedgraphically.Theinfluenceofthefractionalorderparameteronthemisevaluatedanddiscussed.
