Variational principle, uniqueness and reciprocity theorems for higher order time-fractional four-phase-lag generalized thermoelastic diffusion model

Abstract

In the present paper, a variational principle is derived for the recently introduced higher order time-fractional four-phase-lag generalized thermoelastic diffusion model for a linear, isotropic and homogeneous thermoelastic diffusive continuum. Then uniqueness of the solution for the governing field equations of the considered model is proved under suitable conditions. Finally a reciprocity theorem is obtained for the said model.

Keywords:

• Four-phase-lag generalized thermoelastic diffusion
• higher order time-fractional Caputo derivative
• reciprocity theorem
• uniqueness theorem
• variational principle

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 74F

Acknowledgements

The authors would like to express their sincere thanks to the referees for helpful comments and suggestions for the improvement of this paper.