Fractional analysis for nonlinear electrical transmission line and nonlinear Schroedinger equations with incomplete sub-equation

Abstract

We use the fractional complex transform with the modified Riemann-Liouville derivative operator to establish the exact and generalized solutions of two fractional partial differential equations. We determine the solutions of fractional nonlinear electrical transmission lines (NETL) and the perturbed nonlinear Schroedinger (NLS) equation with the Kerr law nonlinearity term. The solutions are obtained for the parameters in the range ( $0<\alpha\le 1$ ) of the derivative operator and we found the traditional solutions for the limiting case of $\alpha =1$ . We show that according to the modified Riemann-Liouville derivative, the solutions found can describe physical systems with memory effect, transient effects in electrical systems and nonlinear transmission lines, and other systems such as optical fiber.