Fractional Nonlocal Elasticity

Nonlocal elasticity assumes integral stress constitutive equationConstitutive equation, takes into account interatomic long-range forces, reduces to the classical theory of elasticity in the long wave-lenght limit and to the atomic lattice theory in the short wave-length limit. In this chapter, we describe the nonlocal elasticity theory with the kernel (the weight function in the integral stress constitutive equation) being the Green function of the Cauchy problemCauchy problem for the fractional diffusion (heat conduction) equation with the Caputo and Riesz derivatives. The solutions for the straight screw and edge dislocations and point defectPoint defect  in an infinite solid are obtained in the framework of the proposed theory.