Exact Solution of System of Multi-Photograph Type Delay Differential Equations Via New Algorithm Based on Homotopy Perturbation Method


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Authors

  • Nidal Anakira Sohar University
  • M. J. Mohammed
  • Irianto Irianto
  • Ala Amourah
  • osama Oqilat

Keywords:

HPM Procedure, Series Expansion, Laplace Trans-form, Pade Approximant, Pantograph equations

Abstract

A new algorithm is proposed in this paper to explain how the modified homotopy perturbation approach can be successfully implemented based on the Pade approximants and the Laplace transformin order to acquire the accurate solutions of a nonlinear system of multiphotographdelay differential equations. The method that has been suggestedhas the benefit of giving exact solutions, and it is simple to implementanalytically on the issues that have been presented. Examples have been provided to demonstrate that this strategy may be utilized andis successful in its application. The results show that the method thatwas described could be used to solve many different types of differential equations.

References

Yu, Z. H. (2008). Variational iteration method for solving the multi-pantograph delay equation. Physics Letters A,

(43), 6475–6479.

Saadatmandi, A., & Dehghan, M. (2009). Variational iteration method for solving a generalized pantograph equation.

Computers & Mathematics with Applications, 58(11–12), 2190–2196.

Bahgat, M. S. (2020). Approximate analytical solution of the linear and nonlinear multi-pantograph delay differential

equations. Physica Scripta, 95(5), 055219.

Ezz-Eldien, S. S. (2018). On solving systems of multi-pantograph equations via spectral tau method. Applied

Mathematics and Computation, 321, 63–73.

Sezer, M., & Sahin, N. (2008). Approximate solution of multi-pantograph equation with variable coefficients. Journal

of Computational and Applied Mathematics, 214(2), 406–416.

Anakira, N., Jameel, A., Hijazi, M., Alomari, A. K., & Man, N. (2022). A new approach for solving multi-pantograph

type delay differential equations. International Journal of Electrical & Computer Engineering (2088–8708), 12(2).

Ibrahim, R. W., Ahmad, M. Z., & Mohammed, M. J. (2016). Generalized population dynamic operator with delay based

on fractional calculus. Journal of Environmental Biology, 37(5), 1139.

Yu, Z. H. (2008). Variational iteration method for solving the multi-pantograph delay equation. Physics Letters A,

(43), 6475–6479.

Anakira, N. R. (2018). Optimal homotopy asymptotic method for solving multi-pantograph type delay differential

equations. Adv. Differ. Equ. Control Proc. 19(3), 191–204.

Jameel, A. F., Anakira, N. R., Alomari, A. K., Al-Mahameed, M., & Saaban, A. (2019). A new approximate solution of

the fuzzy delay differential equations. International Journal of Mathematical Modelling and Numerical Optimisation,

(3), 221–240.

Anakira, N. R., Alomari, A. K., & Hashim, I. (2013, November). Application of optimal homotopy asymptotic method for

solving linear delay differential equations. In AIP Conference Proceedings (Vol. 1571, No. 1, pp. 1013–1019). American

Institute of Physics.

Bahgat, M. S., & Sebaq, A. M. (2021). An Analytical Computational Algorithm for Solving a System of Multipantograph

DDEs Using Laplace Variational Iteration Algorithm. Advances in Astronomy, 2021.

Jameela, A., Anakira, N. R., Alomari, A. K., Hashim, I., & Shakhatreh, M. A. (2016). Numerical solution of n’th order

fuzzy initial value problems by six stages. Journal of Nonlinear Science Applications, 9(2), 627–640.

Jameel, A. F., Shather, A. H., Anakira, N. R., Alomari, A. K., & Saaban, A. (2020). Comparison for the approxi-

mate solution of the second-order fuzzy nonlinear differential equation with fuzzy initial conditions. Mathematics and

Statistics, 8(5), 527–534.

Anakira, N. R., Abdelkarim, H., & Abu-Dawas, M. (2020). Homotopy Sumudu transformation method for solving frac-

tional delay differential equations. Gen. Lett. Math, 9(1), 33–41.

Biazar, J., Ghazvini, H., & Eslami, M. (2009). He’s homotopy perturbation method for systems of integro-differential

equations. Chaos, Solitons & Fractals, 39(3), 1253–1258.

Abdulaziz, O., Hashim, I., & Momani, S. (2008). Solving systems of fractional differential equations by homotopy-per-

turbation method. Physics Letters A, 372(4), 451–459.

Al-Ahmad, S., Anakira, N. R., Mamat, M., Suliman, I. M., & AlAhmad, R. (2021). Modified differential transformation

scheme for solving classes of non-linear differential equations. TWMS J. App. and Eng. Math, 12(1), pp. 107–119.

Rabbani, M. (2013). New homotopy perturbation method to solve non-linear problems. J. Math. Comput. Sci, 7(1),

–275.

Shather, A. H., Jameel, A. F., Anakira, N. R., Alomari, A. K., & Saaban, A. (2021). Homotopy analysis method approx-

imate solution for fuzzy pantograph equation. International Journal of Computing Science and Mathematics, 14(3),

–300.

Saadeh, R. A. N. I. A. (2022). A reliable algorithm for solving system of multi-pantograph equations. WSEAS Trans.

Math, 21, 792–800.

Komashynska, I., Al-Smadi, M., Al-Habahbeh, A., & Ateiwi, A. (2016). Analytical approximate solutions of systems of

multi-pantograph delay differential equations using residual power-series method. arXiv preprint arXiv:1611.05485.

Davaeifar, S., & Rashidinia, J. (2017). Solution of a system of delay differential equations of multi pantograph type.

Journal of Taibah University for Science, 11(6), 1141–1157.

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Published

2024-06-03

How to Cite

Anakira, N., M. J. Mohammed, Irianto Irianto, Ala Amourah, & osama Oqilat. (2024). Exact Solution of System of Multi-Photograph Type Delay Differential Equations Via New Algorithm Based on Homotopy Perturbation Method. Results in Nonlinear Analysis, 7(2), 187–197. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/406

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