Abstract
This study aims at seeking a fractional-order equation that is a good approximation for a delay equation. To this end, we consider a delay equation with simple initial and boundary conditions and obtain a fractional-order equation and an associated numerical method for approximating the solution of the delay equation. In order to determine the fractional-order equation that is a better approximation of the Delay equation, the Levenberg-Marquardt iterative method is employed to estimate the optimal parameters in the fractional-order equation. This obtained fractional-order equation is then tested and compared its solution with the solution of the delay equation. Results show that the fractional method is indeed a good approximation for the Delay equation.
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