Numerical Solution of Linear Fractional Differential Equation with Delay Through Finite Difference Method

Auras K.  Hameed; Muna M.  Mustafa

doi:10.24996/ijs.2022.63.3.28

Authors

Auras K. Hameed Department of Computer Science, College of Science for Women, University of Baghdad, https://orcid.org/0000-0003-4794-7712
Muna M. Mustafa Department of Mathematics, College of Science for Women, University of Baghdad

DOI:

https://doi.org/10.24996/ijs.2022.63.3.28

Keywords:

Caputo derivative, Delay differential equation, fractional order, finite difference, Trapezoidal rule

Abstract

This article addresses a new numerical method to find a numerical solution of the linear delay differential equation of fractional order , the fractional derivatives described in the Caputo sense. The new approach is to approximating second and third derivatives. A backward finite difference method is used. Besides, the composite Trapezoidal rule is used in the Caputo definition to match the integral term. The accuracy and convergence of the prescribed technique are explained. The results are shown through numerical examples.