Nonlocal fractional laplacian dynamics in stochastic KdV-Burgers-Huxley models with memory: A cauchy Principal-Value euler wavelet approach

Document Type

Article

Source of Publication

Communications in Nonlinear Science and Numerical Simulation

Publication Date

11-1-2026

Abstract

This paper develops an Euler wavelet collocation framework for partial differential equations involving the fractional Laplacian. The fractional operator is treated directly through its Cauchy principal-value formulation, which preserves the nonlocal character of the model and avoids relying on finite-difference stencils or purely quadrature-based approximations. Since the Euler wavelet basis admits exact integration, the resulting fractional Laplacian matrix can be assembled efficiently and with high numerical precision. The method is tested on several benchmark problems with known analytical solutions, including extended Dirichlet problems and regularized fundamental solutions, in both subdiffusive and superdiffusive regimes. The numerical results show high numerical accuracy and demonstrate that the error is strongly influenced by the fractional order, as expected from the singular structure of the fractional kernel. The framework is then applied to a stochastic fractional Korteweg-de Vries-Burgers-Huxley equation with memory effects. The simulations indicate that the proposed scheme remains stable for different initial profiles and noise intensities, while capturing the combined influence of nonlocal diffusion, stochastic forcing, and hereditary memory. Overall, the results support the effectiveness of the Euler wavelet collocation approach for nonlinear, nonlocal, and stochastic fractional models.

ISSN

1007-5704

Publisher

Elsevier BV

Volume

163

Disciplines

Mathematics

Keywords

Collocation methods, Euler wavelets, Fractional laplacian, Nonlocal operators, Stochastic partial differential equations

Scopus ID

105052407369

Indexed in Scopus

yes

Open Access

no

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