A New Collocation Method for Solving Fractional Pantograph Differential Equations Based on the Fractional Cα Space

Zhang Haizhen

（Shanwei Polytechnic,Shanwei 516600）

Abstract：In this paper,a new collocation method based on fractional spline is proposed for solving fractional pantograph differential equations.For solving the equation,the difficulties lie in choosing the space of the exact solution.In this paper,we solve the issue perfectly by proposing the concept of the fractional space.Meanwhile,a base of this fractional space is obtained.Based on the fractional space,a strict theory for obtaining the approximate solution is established.Finally,some examples are discussed for demonstrating the validity and applicability of our method and a small amount of calculation can gain an accurate number which satisfies the application requirements.

Key words:Collocation method;Fractional order;Differential equations;Pantograph delay;Fractional space