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An extended Kudryashov technique for solving stochastic nonlinear models with generalized conformable derivatives. (English) Zbl 1458.60073

Summary: 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.

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35Q53 KdV equations (Korteweg-de Vries equations)
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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