A numerical method for fractional variable order pantograph differential equations based on Haar wavelet

Abstract

In this article, Haar wavelet collocation technique is developed for the solution of variable order fractional pantograph differential equations. The Haar technique reduces the given equations into a system of linear algebraic equations. The derived system is then solved by Gaussian elimination method. Through fixed point theory, we develop some requisite conditions for the existence of at most one solution of the underlying problem endowed with initial conditions. Some numerical examples are also given for checking the validation and convergence of the concerned method. The mean square root and maximum absolute errors for different number of collocation points have been calculated. The results indicate that Haar method is efficient for solving such equations. Fractional derivative is described in the Caputo sense.