Solution of optical soliton nonlinear fractional differential equations

This study is consisted of six parts. In first section, the development of nonlinear fractional differential equations, solitons and their informational expressions and solutions as existing in the literature are discussed in detail. In second section, necessary definitions and theorems that shed light on our work are given. In third section, the general structures of The Extended ShGEEM, -Expansion Method, and - Expansion Method and the solution steps of these methods are discussed. In fourth section, The Extended Sinh-Gordon Expansion Method (ShGEEM) was applied to obtain the exact solutions of the (2+1)-dimensional cubic nonlinear Schrodinger equation with fractional temporal evolution. Secondly, the ShGEEM method was applied to obtain analytical solutions of the time-fractional Radhakrishnan-Kundu-Lakshmanan equation. Finally, the - Expansion method and - Expansion method are applied to find the exact solutions of the M-fractional (2+1)-dimensional Davey-Stewartson equation. 2D and 3D graphics are available for all methods applied to the equations under consideration, and the graphics are shown with the help of Wolfram Mathematica. In the fiveth chapter, includes findings and discussion. In this last section, the solutions in our study are different from the existing studies in the literature, and a comprehensive conclusion is given about how the program can be useful for other fractional differential equations.