On plane Λ-fractional linear elasticity theory

Abstract

ABSTRACT: Non-local plane elasticity problems are discussed in the context of Λ-fractional linear elasticity theory. Adapting the Λ-fractional derivative along with the Λ-fractional space, where geometry and mechanics are valid in the conventional way, non-local plane elasticity problems are solved with the help of biharmonic functions. Then, the results are transferred into the initial plane. Applications are presented to homogeneous and the fractional beam bending problem.

Keywords

• Plane elasticity problems
• Λ-fractional linear elasticity theory
• Λ-fractional derivative
• Λ-fractional space
• Biharmonic function
• Fractional beam bending