Effective transform-expansions algorithm for solving non-linear fractional multi-pantograph system

Ahmad Qazza; Rania Saadeh; Osama Ala'yed; Ahmad El-Ajou; Ahmad Qazza; Rania Saadeh; Osama Ala'yed; Ahmad El-Ajou

doi:10.3934/math.20231017

AIMS Mathematics

2023, Volume 8, Issue 9: 19950-19970. doi: 10.3934/math.20231017

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Effective transform-expansions algorithm for solving non-linear fractional multi-pantograph system

1.
Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan
2.
Department of Mathematics, Jadara University, Irbid 21110, Jordan
3.
Department of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, Jordan

Received: 23 March 2023 Revised: 23 May 2023 Accepted: 06 June 2023 Published: 15 June 2023
MSC : 26A33, 34K37, 40G10

This study presents a new and attractive analytical approach to treat systems with fractional multi-pantograph equations. We introduce the solution as a rapidly-converging series using the Laplace residual power series technique. This method controls the range of convergence and can be easily programmed to find many terms of the series coefficients by computer software. To show the efficiency and strength of the proposed method, we compare the results obtained in this study with those of the Homotopy analysis method and the residual power series technique. Furthermore, two exciting applications of fractional non-homogeneous pantograph systems are discussed in detail and solved numerically. We also present graphical simulations and analyses of the obtained results. Finally, we conclude that the obtained approximate solutions are very close to the exact solutions with a slight difference.
- Caputo fractional derivative,
- multi-pantograph equations,
- Laplace residual power series method
Citation: Ahmad Qazza, Rania Saadeh, Osama Ala'yed, Ahmad El-Ajou. Effective transform-expansions algorithm for solving non-linear fractional multi-pantograph system[J]. AIMS Mathematics, 2023, 8(9): 19950-19970. doi: 10.3934/math.20231017

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Abstract

This study presents a new and attractive analytical approach to treat systems with fractional multi-pantograph equations. We introduce the solution as a rapidly-converging series using the Laplace residual power series technique. This method controls the range of convergence and can be easily programmed to find many terms of the series coefficients by computer software. To show the efficiency and strength of the proposed method, we compare the results obtained in this study with those of the Homotopy analysis method and the residual power series technique. Furthermore, two exciting applications of fractional non-homogeneous pantograph systems are discussed in detail and solved numerically. We also present graphical simulations and analyses of the obtained results. Finally, we conclude that the obtained approximate solutions are very close to the exact solutions with a slight difference.

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