Analytic Fuzzy Formulation of a Time-Fractional Fornberg–Whitham Model with Power and Mittag–Leffler Kernels

This manuscript assesses a semi-analytical method in connection with new hybrid fuzzy integral transform and the Adomian decomposition via notion of fuzziness known as Elzaki (briefly, EADM). Moreover, we use aforesaid strategy to address time-fractional Fornberg–Whitham equation (FWE) under gH-differentiability by employing different initial conditions (IC). Several algebraic aspects Caputo fractional derivative (CFD) Atangana–Baleanu (AB) operator sense, respect transform, are presented validate their utilities. Apart from that, general algorithm for AB derivatives sense is proposed. Some illustrative cases demonstrated understand algorithmic approach FWE. Taking into consideration uncertainty parameter ??[0,1] various orders, convergence error analysis reported graphical representations FWE that have close harmony closed form solutions. It worth mentioning projected verify supremacy reliability configuring numerical solutions nonlinear partial differential equations arising physical complex structures.