In this paper, we propose the fuzzy Shehu transform method (FSTM) using Zadeh’s decomposition theorem and fuzzy Riemann integral of real-valued functions on finite intervals. As an alternative to standard fuzzy Laplace transform and the fuzzy Sumudu integral transform, we established some potential useful (new or known) properties of the FSTM and validate their applications. Furthermore, the FSTM is coupled with the well-known homotopy analysis method to obtain the approximate and exact solutions of fuzzy differential equations of integer and non-integer order derivatives. The convergence analysis and the error analysis of the suggested technique are provided and supported by graphical solutions. Comparison of the numerical simulations of exact and approximate solutions of two fuzzy fractional partial differential equations are tabulated to further justify the reliability and efficiency of the proposed method.

在本文中，我们基于Zadeh分解定理和有限区间上实值函数的模糊Riemann积分，提出了模糊Shehu变换方法（FSTM）。作为标准模糊拉普拉斯变换和模糊Sumudu积分变换的替代方法，我们建立了FSTM的某些潜在有用（新的或已知的）特性，并验证了它们的应用。此外，FSTM与众所周知的同伦分析方法相结合，以获得整数和非整数阶导数的模糊微分方程的近似和精确解。图形化解决方案提供并支持了所建议技术的收敛性分析和误差分析。