Fuzzy Yang transform for second order fuzzy differential equations of integer and fractional order

Abstract

Abstract In this work, a Laplace-like transform in a fuzzy environment called Yang transform is introduced to solve fuzzy differential equations (FDEs) with the order θ ∈ (1, 2] involving the Caputo fractional derivative in the sense of gH-differentiability. Some basic properties of Yang transform for integer and fractional derivatives are also provided. Furthermore, by utilizing the combination between the Adomian decomposition method (ADM) and the Yang transform method, a general algorithm called the hybrid Yang transform method (HYTM) to solve the solutions of FDEs in the nonlinear form is proposed. For the validity and accuracy of this novel method, some examples and their simulations are given.