A mechanical approach to fractional non-localthermoelasticity

In recent years fractional di erential calculus applications have been developed in physics,chemistry as well as in engineering elds. Fractional order integrals and derivatives ex-tend the well-known de nitions of integer-order primitives and derivatives of the ordinarydi erential calculus to real-order operators.Engineering applications of these concepts dealt with viscoelastic models, stochastic dy-namics as well as with the, recently developed, fractional-order thermoelasticity [3]. Inthese elds the main use of fractional operators has been concerned with the interpolationbetween the heat ux and its time-rate of change, that is related to the well-known secondsound e ect. In other recent studies [2] a fractional, non-local thermoelastic model has beenproposed as a particular case of the non-local, integral, thermoelasticity introduced at themid of the seventies [1].In this study the autors aim to provide a mechanical framework to account for fractional,non-local e ects in thermoelasticity. A mechanical model that corresponds to long-rangeheat ux is introduced and, on this basis, a modi ed version of the Fourier heat ux equa-tion is obtained. Such an equation involves spatial Marchaud fractional derivatives of thetemperature eld as well as Riemann-Liouville fractional derivatives of the heat ux withrespect to time variable to account for second sound effects.