Solution for generalized fuzzy fractional Kortewege-de Varies equation using a robust fuzzy double parametric approach

• The nonlinear KdV equation is a functional description for modeling ion-acoustic waves in plasma and long internal waves in a density-stratified ocean. • This paper proposes the q-HASTM for generalized fuzzy fractional KdV equation. • The fuzzy velocity profiles at different spatial positions with crisp and fuzzy conditions are investigated. • The obtained results are compared with existing works to confirm effectiveness of the method. The nonlinear Kortewege-de Varies (KdV) equation is a functional description for modelling ion-acoustic waves in plasma, long internal waves in a density-stratified ocean, shallow-water waves and acoustic waves on a crystal lattice. This paper focuses on developing and analysing a resilient double parametric analytical approach for the nonlinear fuzzy fractional KdV equation (FFKdVE) under gH-differentiability of Caputo fractional order, namely the q -Homotopy analysis method with the Shehu transform ( q -HASTM). A triangular fuzzy number describes the Caputo fractional derivative of order α , 0 < α ≤ 1 , for modelling problem. The fuzzy velocity profiles with crisp and fuzzy conditions at different spatial positions are investigated using a robust double parametric form-based q -HASTM with its convergence analysis. The obtained results are compared with existing works in the literature to confirm the efficacy and effectiveness of the method.