On Λ-Fractional peridynamic mechanics

Abstract

Λ-Fractional Mechanics has already been introduced since it combines non-locality with mathematical analysis. It is well established, that conventional mechanics is not a proper theory for describing various phenomena in micro or nanomechanics. Further, various experiments in viscoelasticity, fatigue, fracture, etc., suggest the introduction of non-local mathematical analysis in their description. Fractional calculus has been used in describing those phenomena. Nevertheless, the well-known fractional derivatives with their calculus fail to generate differential geometry, since the established fractional derivatives do not fulfill the prerequisites of differential topology. A Λ-fractional analysis can generate geometry conforming to the prerequisites of differential topology. Hence Λ-fractional mechanics deals with non-local mechanics, describing the various inhomogeneities in various materials with more realistic rules.

Keywords

• fractional-order
• fractional integral
• fractional derivative
• riemann-liouville fractional derivative
• λ-fractional space
• λ-fractional derivative
• left and right λ-spaces
• fractional peridynamics
• fractional horizon