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

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.