Fractional Wave Equations

Abstract

Time fractional wave equations, where the ordinary second derivative is substituted by a fractional one of order 1 < μ < 2, have attracted attention especially in the dynamical theory of linear viscoelasticity, in the description of the propagation of stress waves in viscoelastic media, for analysis of the fractional diffusive waves in viscoelastic solids which exhibit a power-law creep, and to describe the power-law attenuation with frequency when sound waves travel through inhomogeneous media. Fractional wave equation is also used as a model for oscillation of a cable made of special smart materials. Thus, in this chapter we further include a friction due to the interaction of the cable with given complex environment, as well as an external force acting on the cable.