On fuzzy valued fractional iterative schemes

Abstract

This work provides a two-step fractional iterative algorithm for fuzzy nonlinear equations (FNEs). The proposed algorithm combines the memory effect of the fractional derivatives and the uncertainty representation of the fuzzy numbers through the use of fractional calculus and fuzzy logic, respectively. Convergence analysis reveals that the method is of order 49. Numerical experiments involving a real-world profit-maximization problem affirm the accuracy and better convergence as compared to the classical and fractional Newton methods. Numerical examples and their graphical illustrations of the fuzzy solutions, absolute errors, and functional values also help to argue for the efficiency and reliability of the given technique.