31662be5-436d-4ce5-94a2-39a851c7748b20221201082211252wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON MATHEMATICS2224-28801109-276910.37394/23206http://wseas.org/wseas/cms.action?id=40511520221520222110.37394/23206.2022.21https://wseas.com/journals/mathematics/2022.phpRaniaSaadehDepartment of Mathematics, Zarqa University, Zarqa 13110, JORDANIn this article, a new series solution of a system of pantograph equations is established using the residual power series method (RPSM). The proposed method produces the solution in terms of a convergent infinite series, requiring no linearization, perturbation or discretization, in some cases it reproduces the exact solutions. We apply the RPSM to solve the multi-pantograph equations, and we show that the outcomes are very accurate. Some examples are given to demonstrate the simplicity and efficiency of the proposed method. Comparisons to the Laplace decomposition approach are made to verify the efficiency and applicability of the presented method in solving similar problems.1212022121202279280091https://wseas.com/journals/mathematics/2022/b845106-1733.pdf10.37394/23206.2022.21.91https://wseas.com/journals/mathematics/2022/b845106-1733.pdf10.1098/rspa.1971.0078J.R. Ockendon, A.B. Tayler, The dynamics of a current collection system for an electric locomotive, Proc. R. Soc. Lond. Ser. A. 322 (1971) 447-468. 10.1016/j.aej.2022.04.004Saadeh R, Burqan A, El-Ajou A. Reliable solutions to fractional Lane-Emden equations via Laplace transform and residual error function. Alexandria Engineering Journal. 2022 Dec 1;61(12):10551-62. 10.3390/axioms11100572Abu-Ghuwaleh M, Saadeh R, Qazza A. A Novel Approach in Solving Improper Integrals. Axioms. 2022 Oct 20;11(10):572. 10.3390/math10193547Abu-Ghuwaleh M, Saadeh R, Qazza A. General Master Theorems of Integrals with Applications. 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