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Abstract
In this thesis, the one-step Adams-Bashforth-Moulton (ABM) predictor-corrector method is introduced to solve the initial value problems (IVPs) of nonlinear fractional delay di{uFB00}erential equations (FDDEs). Moreover, this method is ex- tended to solve the variable-order FDDEs, where the derivative is de{uFB01}ned in the Caputo variable-order fractional sense. Special attention is given to study the error estimate of the proposed method. Numerical test examples are presented to demonstrate utility of the method, one of these examples is the variable- order fractional delay version of the Chen system. All numerical results are obtained in this thesis using MATLAB R2013a.