Application of the restricted fractional differential transform for Solve linear fractional integro-differential equations

Abstract

In 2007, Arikoglu and Ozkol developed a new semi-analytical numerical technique, fractional differential
transform method (FDTM), for solving fractional differential equations (FDEs) and then developed it to
solve fractional integro-differential equations (FIDEs). In fact, when the order of fractional derivative is
irrational, FDTM was not achieved for solving both FDEs nor FIDEs. In 2017, Ayad et al. propose a new
method, restricted fractional differential transform method (RFDTM), to be appropriate for solving rational
or irrational order FDEs. In this study, we establish a new theorems to extend the RFDTM to solve linear
FIDEs. Some illustrated examples are investigated to demonstrate the theoretical results.