Examination of the conformable fractional Noyes Field model

Khalil and his colleagues introduced a new definition for fractional derivative and fractional integral in 2014. They named it the compatible fractional order derivative and integral. After the introduction of this compatible definition, many differential equations involving compatible derivatives have been solved analytically or numerically in the literature. The original contribution of this thesis is the combination of the q-homotopy analysis transformation method with the compatible fractional order and the Sawi integral transformation. Additionally, a new method will be introduced to the literature, which is expected to yield better results for existing compatible partial differential equations. The q-homotopy Sawi analysis transformation method will be theoretically obtained for this new compatible meaning, and numerical solutions of the Noyes-Field model with fractional order will be obtained using this method. Furthermore, the numerical solutions obtained will be compared with the analytical solutions and analyzed for errors. The graphs of these numerical solutions will be drawn using the MAPLE software program.