@article{Lazopoulos2022, 
author = {K.A. Lazopoulos and E. Sideridis and A.K. Lazopoulos},
title = {On Λ-Fractional peridynamic mechanics},
year = {2022},
journal = {AIMS Materials Science},
volume = {9},
number = {5},
pages = {684-701},
keywords = {Fractional-order, Fractional Derivative, Fractional Integral, Riemann-Liouville Fractional derivative, Λ-fractional space, Λ-fractional derivative, left and right Λ-spaces, fractional peridynamics, fractional horizon},
url = {https://www.sciopen.com/article/10.3934/matersci.2022042},
doi = {10.3934/matersci.2022042},
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.}
}