On the fractional deformation of a linearly elastic bar

Abstract

Fractional derivatives have non-local character, although they are not mathematical derivatives, according to differential topology. New fractional derivatives satisfying the requirements of differential topology are proposed, that have non-local character. A new space, the Λ-space corresponding to the initial space is proposed, where the derivatives are local. Transferring the results to the initial space through Riemann-Liouville fractional derivatives, the non-local character of the analysis is shown up. Since fractional derivatives have been established, having the mathematical properties of the derivatives, the linearly elastic fractional deformation of an elastic bar is presented. The fractional axial stress along the distributed body force is discussed. Fractional analysis with horizon is also introduced and the deformation of an elastic bar is also presented.

Keywords

• λ-fractional derivative
• λ-fractional space
• fractional stress
• fractional deformation
• fractional body forces
• fractional strain
• fractional horizon