Nagma Younes Ali Daw Kajaman <br/><br/>
Numerical studies for fractional- order delay dierential equations /  
 دراسات عددية للمعادلات التفاضلية المتأخرة من الرتب الكسرية 
Nagma Younes Ali Daw Kajaman ; Supervised Laila F. Abdelal ,  Nasser H. Sweilam 
 - Cairo :   Nagma Younes Ali Daw Kajaman ,   2014 
 - 89 P. :   charts ;   25cm 
<br/><br/>Thesis (M.Sc.) - Cairo University - Faculty of Science - Department of Mathematics  
<br/><br/> 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 dierential equations (FDDEs). Moreover, this method is ex- tended to solve the variable-order FDDEs, where the derivative is dened 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.    
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<br/><br/><label>Subjects--Index Terms: </label>Adams-Bashforth  Delay dierential equations  Fractional calculus