A remark on the q-fractional order differential equations

摘要

An analytical method to obtain the exact solution of q-fractional order differential equations was presented in article Koca (2015) which shows that: “Solving a q-fractional order differential equation is equivalent to solve a q-integer order differential equation”. In this article, we first show that the analytical method given in [3] is wrong. Then, we propose analytical and numerical methods for the Caputo type q-fractional differential equations by using the q-beta function. Some examples are given to disconfirm the solving method in [3] and valid the effectiveness of our methods.