This paper presents an innovative approach to solving the system of fuzzy partial differential equations of fractional order (F-FPDEs) using an iterative method based on the \(\upalpha \) parameter derived from the new iterative method (NIM), called \(\upalpha \) -parameter new iterative method ( \(\upalpha \) -PNIM). Incorporating fuzzy logic helps expand the range of solutions, providing greater flexibility and comprehensiveness compared to traditional solutions. The best value of the \(\upalpha \) parameter is determined using the Black-Winged Kite Algorithm (BKA), which relies on the approximate formula resulting from \(\upalpha \) -PNIM as a fitness function, leading to improved accuracy of solutions compared to conventional \(\upalpha \) selection methods. The new method is known as \(\upalpha ^{\textrm{BK}}\) -PNIM, and it is characterized by its ability to provide accurate and reliable solutions without the need for restrictive hypotheses or prior assumptions compared to NIM. The mean squared error (MSE) and error reminder (ER) were calculated for a set of linear and nonlinear system of F-FPDEs to verify the method’s effectiveness. The results showed that \(\upalpha ^{\textrm{BK}}\) -PNIM offers significant improvements in solution accuracy over NIM, making it a powerful and effective tool for dealing with complex equations involving fuzziness and fractional orders.
