Fractional view analysis of delay differential equations via numerical method

M. Mossa Al-Sawalha; Azzh Saad Alshehry; Kamsing Nonlaopon; Rasool Shah; Osama Y. Ababneh; M. Mossa Al-Sawalha; Azzh Saad Alshehry; Kamsing Nonlaopon; Rasool Shah; Osama Y. Ababneh

doi:10.3934/math.20221123

AIMS Mathematics

2022, Volume 7, Issue 12: 20510-20523. doi: 10.3934/math.20221123

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Research article

Fractional view analysis of delay differential equations via numerical method

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
2.
Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
3.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
4.
Department of Mathematics, Abdul Wali Khan University Mardan 23200, Pakistan
5.
Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan

Received: 28 July 2022 Revised: 11 September 2022 Accepted: 12 September 2022 Published: 19 September 2022
MSC : 33B15, 34A34, 35A20, 35A22, 44A10

In this article, we solved pantograph delay differential equations by utilizing an efficient numerical technique known as Chebyshev pseudospectral method. In Caputo manner fractional derivatives are taken. These types of problems are reduced to linear or nonlinear algebraic equations using the suggested approach. The proposed method's convergence is being studied with particular care. The suggested technique is effective, simple, and easy to implement as compared to other numerical approaches. To prove the validity and accuracy of the presented approach, we take two examples. The solutions we obtained show greater accuracy as compared to other methods. Furthermore, the current approach can be implemented for solving other linear and nonlinear fractional delay differential equations, owing to its innovation and scientific significance.
- Chebyshev pseudospectral method,
- Caputo operator,
- fractional pantograph delay differential equations
Citation: M. Mossa Al-Sawalha, Azzh Saad Alshehry, Kamsing Nonlaopon, Rasool Shah, Osama Y. Ababneh. Fractional view analysis of delay differential equations via numerical method[J]. AIMS Mathematics, 2022, 7(12): 20510-20523. doi: 10.3934/math.20221123

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Abstract

In this article, we solved pantograph delay differential equations by utilizing an efficient numerical technique known as Chebyshev pseudospectral method. In Caputo manner fractional derivatives are taken. These types of problems are reduced to linear or nonlinear algebraic equations using the suggested approach. The proposed method's convergence is being studied with particular care. The suggested technique is effective, simple, and easy to implement as compared to other numerical approaches. To prove the validity and accuracy of the presented approach, we take two examples. The solutions we obtained show greater accuracy as compared to other methods. Furthermore, the current approach can be implemented for solving other linear and nonlinear fractional delay differential equations, owing to its innovation and scientific significance.

References

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