A difference method for solving the [formula omitted]-fractional differential equations

Abstract

In this article, we study the Caputo type q-fractional differential equation: cDqαx(t)=f(t,x(t)),0<α,q<1. By using the piecewise linear interpolation approximation, we present a difference formula for discretizing the Caputo type q-fractional derivative cDqαx(t) and derive the truncation error boundness. This difference formula is used to solve the initial value problem of q-fractional differential equation. Numerical examples are provided to verify the effectiveness of our difference method.