A Modified New Iterative Method for Solving Nonlinear Fractional-Order Delay Differential Equations

This paper explores the application of the Modified New Iterative Method (MNIM) to solve nonlinear fractional-order delay differential equations (NFDDEs). A series of test problems are presented to evaluate the method's performance across various fractional orders. The results indicate that MNIM yields highly accurate approximations, particularly when the fractional order approaches an integer. The method is especially effective for integer-order cases and for fractional orders close to them. However, its accuracy decreases as the fractional order becomes smaller, with noticeable errors emerging over larger domains. MNIM remains a powerful and adaptable approach for solving a broad class of fractional differential equations.