White noise theory and general improved Kudryashov method for stochastic nonlinear evolution equations with conformable derivatives

• Main Author: Abd-Allah Hyder
• Format: Article
• Language: English
• Published: SpringerOpen 2020-05-01
• Series: Advances in Difference Equations
• Subjects: Kudryashov method; Combined KdV–mKdV equation; Nonlinear evolution equations; Conformable derivatives; Exact solutions; Stochastic
• Online Access: http://link.springer.com/article/10.1186/s13662-020-02698-7

Abstract The aim of this work is to investigate the Wick-type stochastic nonlinear evolution equations with conformable derivatives. The general Kudryashov method is improved by a new auxiliary equation. So, a new technique, which we call “the general improved Kudryashov method (GIKM)”, is introduced to produce exact solutions for the nonlinear evolution equations with conformable derivatives. By means of GIKM, white noise theory, Hermite transform, and computerized symbolic computation, a novel technique is presented to solve the Wick-type stochastic nonlinear evolution equations with conformable derivatives. This technique is applied to construct exact traveling wave solutions for Wick-type stochastic combined KdV–mKdV equation with conformable derivatives. Moreover, numerical simulations with 3D profiles are shown for the obtained results.