A new fractional mechanics based on fractional addition

Abstract

In this paper we are to define a new velocity having a dimension of (Length)α=(Time) and a new acceleration having a dimension of (Length)α=(Time)2, based on the fractional addition rule. Using this we discuss the fractional mechanics in one dimension. We show the conservation of fractional energy and formulate the Hamiltonian formalism for fractional mechanics. We exhibit some examples of fractional mechanics.