Optical modeling for recursional Hasimoto map with normalized time fractional applications

Abstract

In this paper, we construct the optical flow equations obtained with the help of a timelike curve in De Sitter 2D space S(1)(2 )and with the aid of the Hasimoto map defined by this curve. First, we introduce the Hasimoto map, which we call the De-Hasimoto map, for a timelike curve in S-1(2). Then, with the help of this map and the equation representing the vortex filament motion, we obtain some flow equations with time and arc length parameters. Finally, we compute exact solutions of time fraction of an obtained optical motion equation, and we present some physical reviews on it.