Numerical simulation for fractional delay differential equations

In the present paper we numerically simulate our results for fractional delay differential equations. In delay differential the evolution of state at a time depends on the past time and the delay term in the delay differential model increases the complexity of the model. Fractional models of delay differential equations (DDEs) are very useful for analysing population dynamics, neural networking and physiology. In the present method using chebyshev polynomials the DDE is converted into a system of linear equations. We have also discussed error estimates as well as convergence of the proposed technique. The CPU time taken by the proposed computational method is also written in tabular form. We have used five test problems to demonstrate the fruitfulness of the proposed technique. Results by used technique are plotted for different fractional order and time delay involved in DDEs. The accuracy of the proposed technique is revealed by plotting absolute error figures and comparing results with some existing solutions.

Automated summary

The paper numerically simulates results for fractional delay differential equations, converting DDEs into a system of linear equations using Chebyshev polynomials. Error estimates, convergence of the technique, and CPU time are discussed, along with the accuracy revealed through plotted results and comparison with existing solutions.