RGNAA PublishingCommunications in Nonlinear Analysis2371-79206120190801A Predictor-Corrector Method for Fractional Delay-Differential System with Multiple Lags788891820ENSalemAbdelmalekDepartment of mathematics, University of Tebessa 12002 Algeria.0000-0001-9762-9654RedouaneDouaifiaLaboratory of Mathematics, Informatics and Systems (LAMIS), Larbi Tebessi University – TebessaJournal Article20190703The purpose of this work is to present numerical solutions of variable-order fractional delay differential equations with multiple lags based on the Adams-Bashforth-Moulton method, where the derivative is defined in the Caputo variable-order fractional sense. Since the variable-order fractional derivatives contain classical and fractional derivatives as special cases and also single delay is a special case of multiple delays, several results of references are significantly generalized. The error analysis for this method is given and the effectiveness of the algorithm is highlighted with numerical examples.http://www.cna-journal.com/article_91820_d0b302b5e7fb81cc1bb69b5a1013e558.pdf