On Λ-Fractional Analysis and Mechanics

Abstract

Λ-Fractional analysis was introduced to fill up the mathematical gap exhibited in fractional calculus, where the various fractional derivatives fail to fulfill the prerequisites demanded by differential topology. Nevertheless, the various advantages exhibited by the fractional derivatives, and especially their non-local character, attracted the interest of physicists, although the majority of them try to avoid it. The introduced Λ-fractional analysis can generate fractional geometry since the Λ-fractional derivatives generate differentials. The Λ-fractional analysis is introduced to mechanics to formulate non-local response problems with the demanded mathematical accuracy. Further, fractional peridynamic problems with horizon are suggested.