Restricted fractional differential transform for solving irrational order fractional differential equations

Arikoglu and Ozkol developed a new semi-analytical numerical technique, fractional differential transform method (FDTM), for solving fractional differential equations (FDEs). FDTM was not achieved for solving irrational order fractional differential equations. Here we develop a new method to be applicable for solving rational or irrational order FDEs. This method is called the restricted fractional differential transform method (RFDTM). In fact, RFDTM is based on the restriction of the classical two dimensional differential transform methods. A useful theorem is provided, and Several FDEs are solved by using RFDTM. Moreover, several illustrative examples are presented to demonstrate the accuracy and effectiveness of the proposed method.