Application of Touchard wavelet to simulate numerical solutions to fractional pantograph differential equations

This paper proposes a new operational numerical method based on Touchard wavelets for solving fractional pantograph differential equations. First, we present an operational matrix of fractional integration as well as the fractional derivative of the Touchard wavelets. Then, by approximating the fractional derivative of the unknown function in terms of the Touchard wavelets and also by using collocation method, the original problem is reduced to a system of algebraic equations. Finally, to show the accuracy and the validity of the proposed technique, we provide some numerical examples.