A Modified Iterative Approach for Solving Linear Fractional-Order Delay Differential Equations

Abstract

This paper explores the application of the Modified New Iterative Method (MNIM) for solving linear fractional-order delay differential equations (FDDEs). The method is assessed through illustrative example, showcasing its effectiveness in producing accurate approximations for linear case, particularly when the fractional order approaches an integer. MNIM demonstrates strong performance in solving equations of integer and near-integer fractional order. However, the accuracy declines as the fractional order moves further from an integer, especially over larger intervals. MNIM remains a powerful and adaptable method for handling a broad spectrum of fractional differential equations involving delays.