The fractional q-differential transformation and its application

In this paper, the definitions and operations of the one-dimensional and two-dimensional fractional q-differential transform is proposed. A distinctive feature of the fractional q-differential transform is its ability to solve linear and nonlinear ordinary/partial fractional q-differential equations.

► A new generalization of the differential transform method is developed to solve q-fractional differential equations.
► The definitions and operations of the one-dimensional and two-dimensional fractional q-differential transform is proposed.
► Several concrete problems were tested by applying the new technique and the results have shown remarkable performance.