Homotopy analysis Shehu transform method for solving fuzzy differential equations of fractional and integer order derivatives

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.

Automated summary

The paper introduces a new fuzzy Shehu transform method using Zadeh's decomposition theorem and fuzzy Riemann integral on finite intervals. By combining this method with the homotopy analysis method, it provides effective solutions for fuzzy differential equations of integer and non-integer order derivatives, supported by convergence analysis and error analysis. Numerical simulations of exact and approximate solutions further demonstrate the reliability and efficiency of the proposed method.