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

• Published in: International journal of applied and computational mathematics Vol. 11; no. 5
• Main Authors: El Ghazouani, Aziz, Elomari, M’hamed, Melliani, Said
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.10.2025; Springer Nature B.V
• Subjects: Acoustic waves; Applications of Mathematics; Computational Science and Engineering; Derivatives; Differential equations; Fluid dynamics; Fractional calculus; Initial conditions; Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Nuclear Energy; Operations Research/Decision Theory; Operators (mathematics); Original Paper; Plasma physics; Theoretical; Wave equations; Wave propagation; Fuzzy fractional acoustic waves models; Caputo generalized Hukuhara fractional derivative; Fuzzy Laplace like transform; Adomian decomposition
• ISSN: 2349-5103; 2199-5796
• DOI: 10.1007/s40819-025-02000-x

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.