Fuzzy fractional Caputo-type numerical scheme for solving fuzzy nonlinear equations

Numerous real-world scenarios can be adequately described by fuzzy fractional calculus in a wide range of scientific disciplines, including natural sciences, social sciences, electrical, chemical, and mechanical engineering, economics, statistics, weather forecasting, and in particular biomedical engineering. In this paper, we proposed a Caputo-type fractional Newton's method for solving fuzzy nonlinear equations. The order of convergence of the proposed methods is σ+1, as shown by convergence analysis. The numerical results of the test examples illustrate that the newly proposed method performs better than other classical fractional iterative schemes previously used in the literature in terms of residual error, computing time, computational order of convergence, basins of attraction, efficiency, and absolute error.