Abstract
In this paper, we will analyze the Regularized Long Wave-Burgers equation with conformable derivative (cd). Some white noise functional solutions for this equation are obtained by using white noise analysis, Hermite transforms, and the modified sub-equation method. These solutions include exact stochastic trigonometric functions, hyperbolic functions solutions and wave solutions.This study emphasizes that the modified fractional sub-equation method is sufficient to solve the stochastic nonlinear equations in mathematical physics.
Highlights
1 Introduction Recently, fractional calculus gained considerable interests and significant theoretical developments in many fields and many studies have been achieved in this field [1,2,3,4,5,6,7,8,9,10,11,12,13,14]
Due to the fact that the stochastic models are more realistic than the deterministic models, we concentrate our study in this paper on the Wick-type stochastic time-fractional Regularized Long Wave-Burgers equation (RLWBE) with conformable derivative
In order to obtain the exact solutions of the random RLWBE with conformable derivative, we only consider it in a white noise environment, that is, we will discuss the Wick-type stochastic RLWBE (1.2)
Summary
Fractional calculus gained considerable interests and significant theoretical developments in many fields and many studies have been achieved in this field [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. Due to the fact that the stochastic models are more realistic than the deterministic models, we concentrate our study in this paper on the Wick-type stochastic time-fractional Regularized Long Wave-Burgers equation (RLWBE) with conformable derivative (cd). In [19] are obtained some solutions of this equation by using the modified Kudryashov method. The cd operator was exposed in [25] This derivative operator can reform the failures of the other definitions. This important operator is the easiest, most natural and effectual definition of the fractional derivative for order η ∈ (0, 1). The definition represents a natural formation of normal derivatives. The definition for 0 ≤ η < 1 gives the classical expressions on polynomials
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