In this paper, we 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. We then discuss the fractional mechanics in one dimension. We show the conservation of fractional energy, and formulate the Hamiltonian formalism for the fractional mechanics. As a matter of illustration, we exhibit some examples for the fractional mechanics.
A generalized form of 't Hooft-Nobbenhuis Complex space-time Transformation is applied on momentum space from which a new model of Deformed Special Relavity at Planck Scale is proposed. The model suggests an energy-dependent Planck's "constant" that vary in space and time and Quantum Mechanics as a low-energy approximation of perhaps a more fundamental theory at Planck Scale.
Doubly special relativity(DSR) introduce a minimal length scale i.e. the Planck length scale, which is independent length scale in addition to the speed of light in the normal special theory of relativity(STR). Doubly special relativity leads to study the $κ$-Minkowski space-time. In this paper, we present the result of our investigation on the thermodynamics of photon gas in the $κ$-Minkowski space-time. For studying this, we start with the $κ$-deformed dispersion relation and keep terms upto first order in the deformation parameter $a$ and we study that how does $κ$-deformed dispersion relat…
