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On fractional bending of beams with \(\Lambda \)-fractional derivative

  • K. A. Lazopoulos
  • A. K. LazopoulosEmail author
Original
  • 5 Downloads

Abstract

Introducing the fractional \(\Lambda \)-derivative, with the corresponding \(\Lambda \)-fractional spaces, the fractional beam bending problem is presented. In fact, non-local derivatives govern the beam bending problem that accounts for the interaction of microcracks or materials non-homogeneities, such as composite materials or materials with fractal geometries. The proposed theory is implemented to the fractional bending deformation of a simply supported beam and a cantilever beam under continuously distributed loading.

Keywords

Fractional dimension Fractional integral Fractional derivative Riemann–Liouville fractional derivative \(\Lambda \)-fractional derivative Left and right \(\Lambda \)-spaces 

Notes

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.RafinaGreece
  2. 2.Mathematical Sciences DepartmentHellenic Army AcademyVariGreece

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