Bektaş, Umut; Anaç, Halil

This paper solves fractional differential equations using the Shehu transform in combination with the q-homotopy analysis transform method (q-HATM). As the Shehu transform is only applicable to linear equations, q-HATM is an efficient technique for approximating solutions to nonlinear differential equations. In nonlinear systems that explain the emergence of stripes in 2D systems, the Newell–Whitehead–Segel equation plays a significant role. The findings indicate that the outcomes derived from the tables yield superior results compared to the existing LTDM in the literature. Maple is utilized to depict three-dimensional surfaces and find numerical values that are displayed in a table.

Anaç, Halil; Bektaş, Umut

In this study, numerical solutions to time-fractional coupled Burgers equations are obtained utilizing the q-homotopy Shehu analysis transform method. The definition of fractional derivatives in the sense of Caputo. q-homotopy Shehu analysis transform method is also used to find the numerical solutions of the time-fractional coupled Burgers equations. In addition, the MAPLE software is utilized to plot the graphs of the solutions. These results demonstrate that the presented method is accurate and simple to implement.