On Λ-Fractional Wave Propagation in Solids

Kostantinos A. Lazopoulos () and Anastasios K. Lazopoulos
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Kostantinos A. Lazopoulos: Independent Researcher, 19009 Rafina, Greece
Anastasios K. Lazopoulos: Mathematical Sciences Department, Hellenic Army Academy, 16673 Vari, Greece

Mathematics, 2023, vol. 11, issue 19, 1-8

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: ?-fractional derivative; ?-fractional space; initial space; global stability; coexistence of phases; strain jumping; stress jumping (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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