On a Generalized Wave Equation with Fractional Dissipation in Non-Local Elasticity

Abstract

We analyze wave equation for spatially one-dimensional continuum with constitutive equation of non-local type. The deformation is described by a specially selected strain measure with general fractional derivative of the Riesz type. The form of constitutive equation is assumed to be in strain-driven type, often used in nano-mechanics. The resulting equations are solved in the space of tempered distributions by using the Fourier and Laplace transforms. The properties of the solution are examined and compared with the classical case.

Keywords

• wave propagation
• general fractional derivative of Riesz type
• fractional differential equations