An operational approach for solving fractional pantograph differential equation

The aim of the current paper is to construct the shifted fractional-order Jacobi functions (SFJFs) based on the Jacobi polynomials to numerically solve the fractional-order pantograph differential equations. To achieve this purpose, rst the operational matrices of integration, product, and panto- graph, related to the fractional-order basis, are derived (operational matrix of integration is derived in Riemann{Liouville fractional sense). Then, these matrices are utilized to reduce the main problem to a set of algebraic equa- tions. Finally, the reliability and efficiency of the proposed scheme are demon- strated by some numerical experiments. Also, some theorems are presented on existence of solution of the problem under study and convergence of our method.