Fuzzy fractional Gardner and Cahn–Hilliard equations with the Atangana–Baleanu operator

Abstract

This article focuses on the investigation and computation of solutions to fuzzy fractional-order Cahn–Hilliard and Gardner equations. The study hybridizes the fuzzy Gardner and Cahn–Hilliard equation into two equations using hybrid techniques and the concept of a parametric fuzzy number. To explore these equations, a combination of a novel iterative approach and the Shehu transformation is employed. The article presents detailed procedures for computing a series of solutions to the fractional-order Cahn–Hilliard and Gardner problem. The applied techniques not only offer precision, simplicity, and efficacy but also outperform other existing technologies. Additionally, several examples are solved to validate the proposed theoretical solution.