The numerical solutions of conformable fractional epidemic and conformable fractional smoking models with a new numerical method

A new definition of fractional derivative and fractional integral was given by Khalil et al. in 2014. This new derivative definition is called conformable fractional order derivative. After this conformable definition in the literature, many differential equations containing conformable derivatives have been solved analytically or numerically. The original value of this thesis is; q-homotopy analysis transform method is made conformable fractional order and combined with conformable fractional order Kushare integral transform. Thus, a new hybrid method will be added to the literature. It is expected that better results of conformable partial differential equations existing in the literature will be obtained with this method. Conformable q- Kushare homotopy analysis transform method will be obtained theoretically in this new compatible sense and numerical solutions of conformable fractional order epidemic and compatible fractional order smoking models will be obtained with this method. In addition, the obtained numerical solutions will be compared with the analytical solutions and error analyzes will be made. These numerical solutions will be plotted in the MAPLE software program.