In this article, we used some methods to solve Riemann-type fractional difference equations. Firstly, we use a method that is a composite method based on the successive approximation method with the Sumudu transform. Secondly, we use a method that is a composite method that consists of the homotopic perturbation method with the Sumudu transform. It was found that the results obtained from these combined methods are identical when compared. We also provided theories and illustrative examples to support the research findings