Analytical and numerical solutions of high-dimensional fractional partial differential equations

Partial differential equations often occur in many areas of science and engineering. When some analytical methods that have been widely used to date are examined, some deficiencies such as modeling deficiencies and difficulty in solution processes have been identified in these methods. Numerical approaches have been used to obtain approximate values of the solutions, along with several analytical techniques that have been widely used up to this point. In this thesis, new exact solutions are obtained for the (3+1)-dimensional Camassa-Holm-Kadomtsev-Petviashvili (CHKP) equation using Sub-Equation, Generalized (G'/G)-Expansion and Modified Kudryashov methods. Then, new exact solutions were obtained for the (2+1)-dimensional Kadomtsev–Petviashvili (KP) equation using the modified Kudryashov method. Additionally, new approximate solutions were obtained using the Residual Power Series Method (RPSM). 3D, contour and 2D graphical drawings of some of the obtained solutions are included to examine the dynamic nature of these results. In addition, a table of comparison of approximate solutions of the current equation with exact solutions for certain parameters is presented.