Closed form soliton solutions of three nonlinear fractional models through proposed improved Kudryashov method

Abstract

We introduce a new integral scheme namely improved Kudryashov method for solving any nonlinear fractional differential model. Specifically, we apply the approach to the nonlinear space–time fractional model leading the wave to spread in electrical transmission lines (s-tfETL), the time fractional complex Schrödinger (tfcS), and the space–time M-fractional Schrödinger–Hirota (s-tM-fSH) models to verify the effectiveness of the proposed approach. The implementing of the introduced new technique based on the models provides us with periodic envelope, exponentially changeable soliton envelope, rational rogue wave, periodic rogue wave, combo periodic-soliton, and combo rational-soliton solutions, which are much interesting phenomena in nonlinear sciences. Thus the results disclose that the proposed technique is very effective and straight-forward, and such solutions of the models are much more fruitful than those from the generalized Kudryashov and the modified Kudryashov methods.