Exact solutions of stochastic fractional Korteweg de–Vries equation with conformable derivatives
Hossam A. Ghany, Abd‐Allah Hyder, Mohammed Zakarya
Abstract
We deal with the Wick-type stochastic fractional Korteweg de–Vries (KdV) equation with conformable derivatives. With the aid of the Exp-function method, white noise theory, and Hermite transform, we produce a novel set of exact soliton and periodic wave solutions to the fractional KdV equation with conformable derivatives. With the help of inverse Hermite transform, we get stochastic soliton and periodic wave solutions of the Wick-type stochastic fractional KdV equation with conformable derivatives. Eventually, by an application example, we show how the stochastic solutions can be given as Brownian motion functional solutions.
Topics & Concepts
Conformable matrixKorteweg–de Vries equationHermite polynomialsSolitonMathematical physicsType (biology)MathematicsMathematical analysisPhysicsNonlinear systemQuantum mechanicsEcologyBiologyNonlinear Waves and SolitonsFractional Differential Equations SolutionsNonlinear Photonic Systems