The numerical solutions of some conformable fractional partial differentialequations

This thesis consists of five main parts. In the first part, information is given about the formation and development of the fractional derivative and the conformable fractional derivative. In the second part, the necessary definitions and theorems are written. In the third part, the methods used are mentioned. In the forth part, the conformable fractional order Kuramoto-Sivashinsky (CFOKS) equations, conformable fractional order Whitham-Broer-Kaup (CFOWBK) equations, conformable time-fractional Jaulent-Miodek (CTFJM) system, conformable fractional order Cahn-Allen (CFOCA) equation for conformable q-homotopy analysis transform method (Cq-HATM) new numerical solutions were investigated by using three different methods called conformable fractional Elzaki decomposition method (CFEDM), conformable homotopy perturbation Elzaki transform method (CHPETM). Numerical simulations were performed to verify that these methods are effective and reliable. Comparisons were made between the obtained solutions and the exact solutions. In the last section, it is emphasized that the proposed new three techniques are simple, powerful and effective for solving nonlinear conformable fractional problems.