Pure mathematics

Pantograph

Mathematics

Economic growth

Biology

Algorithm

Mathematical optimization

Engineering

Fractional calculus

Residual

Mathematical analysis

Series (stratigraphy)

Homotopy analysis method

Paleontology

Economics

Convergence (economics)

Computer science

Numerical analysis

Power series

Applied mathematics

Homotopy

Mechanical engineering

Results in Physics

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.

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