1. On Λ-Fractional peridynamic mechanics
- Author
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K.A. Lazopoulos, E. Sideridis, and A.K. Lazopoulos
- Subjects
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 ,Materials of engineering and construction. Mechanics of materials ,TA401-492 - 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.
- Published
- 2022
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