Abstract
•The Kudryashov technique is developed to a new technique called “the extended Kudryashov technique (EKT)”.•The Wick-type stochastic models are examined in the frame of newly conformable derivatives.•New stochastic exact solutions for the conformable mixed KdV-mKd equation are established by the EKT.•Two new kinds of traveling wave solutions, inclusive periodic and soliton solutions are obtained.•Numerical examples in the cases of deterministic and stochastic functions are applied with 3D profiles for the acquired results.
In this work, we utilize a new generalized derivative of conformable type to examine the nonlinear evolution equations in a Wick-type stochastic environment. By a new auxiliary equation, the Kudryashov technique is developed to a new technique called “the extended Kudryashov technique”. The the extended Kudryashov technique is utilized to establish exact solutions for the mixed KdV-mKdV equation in a Wick-type stochastic environment and with a new generalized conformable type derivative. Two new kinds of traveling wave functional solutions, inclusive periodic and soliton wave solutions are obtained. Furthermore, numerical examples in the cases of deterministic and stochastic functions are applied with 3D profiles for the acquired results.