Analytical numerical solutions of the fractional multi-pantograph system: Two attractive methods and comparisons

Abstract

In this paper, we present numerical analytical solutions of a fractional multi-pantograph system by using two attractive methods with rapidly convergence, control of the convergence region and easily software accounts of the infinite series solutions. These methods are: The homotopy analysis and residual power series methods. Furthermore, two important and interesting problems related to the linear nonhomogeneous fractional pantograph system are formulated from the fractional multi-pantograph system and solved numerically and graphically by using the above-mentioned methods. Finally, we show that the approximate and exact solutions are coinciding with a slight difference in error. Keywords: Caputo fractional derivative, Fractional multi-pantograph system, Homptopy analysis method, Residual power series method