A NUMERICAL METHOD FOR VARIABLE ORDER FRACTIONAL PANTOGRAPH DIFERENTIAL EQUATIONS BASED ON MITTAG-LEFFLER POLYNOMIALS

The main aim of this study is to develop Mittag-Leffler polynomials (MLPs) for solving variable order fractional pantograph differential equations. For the MLPs, we obtain the operational matrix of Caputo’s variable order derivative. We also introduced the pantograph operational matrix of MLPs. The equations under concern in this study can be turned into algebraic equations with unknown MLPs coefficients. The superiority of the current approach is demonstrated with some examples, and the results indicate its good results.