On Λ-Fractional Wave Propagation in Solids

Abstract

Wave propagation in solids is discussed, based upon inherently non-local Λ-fractional analysis. Following the governing equations of Λ-fractional continuum mechanics, the Λ-fractional wave equations are derived. Since the variational procedures are only global, in the present Λ-fractional analysis, various jumpings, either in the strain or the stress, may be shown. The proposed theory is applied to impact-induced transitions in two-phase elastic materials and viscoelastic materials.

Keywords

• Λ-fractional derivative
• Λ-fractional space
• initial space
• global stability
• coexistence of phases
• strain jumping