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<p>This paper presents a novel hybrid fuzzy Laplace-like transform method (HFLTM) for solving fuzzy fractional acoustic wave equations involving the Caputo generalized Hukuhara (gH) fractional derivative. By combining Adomian decomposition with fuzzy Laplace-like transforms under gH-differentiability, we develop systematic approaches for solving nonlinear fuzzy fractional differential equations (FFDEs). The method is applied to three classes of fractional acoustic wave models: nonlinear regularized long wave equations and their linear counterparts. Numerical examples demonstrate the effectiveness of the approach, with solutions obtained for triangular fuzzy initial conditions. The proposed technique provides a powerful analytical tool for wave propagation problems under uncertainty, with applications in plasma physics and fluid dynamics.</p>

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Hybrid Fuzzy Laplace-Like Transform Method for Solving the Fuzzy Fractional Acoustic Waves Model Involving the Caputo Generalized Hukuhara Fractional Derivative Operator

  • 期刊论文

  • 发表日期：

    2025年8月11日

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  • Aziz El Ghazouani,
  • M’hamed Elomari,
  • Said Melliani

摘要

This paper presents a novel hybrid fuzzy Laplace-like transform method (HFLTM) for solving fuzzy fractional acoustic wave equations involving the Caputo generalized Hukuhara (gH) fractional derivative. By combining Adomian decomposition with fuzzy Laplace-like transforms under gH-differentiability, we develop systematic approaches for solving nonlinear fuzzy fractional differential equations (FFDEs). The method is applied to three classes of fractional acoustic wave models: nonlinear regularized long wave equations and their linear counterparts. Numerical examples demonstrate the effectiveness of the approach, with solutions obtained for triangular fuzzy initial conditions. The proposed technique provides a powerful analytical tool for wave propagation problems under uncertainty, with applications in plasma physics and fluid dynamics.