On fractional bending of beams with Λ-fractional derivative.

Introducing the fractional Λ -derivative, with the corresponding Λ -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. [ABSTRACT FROM AUTHOR]