Nonlinear Fractional Differential Equations. Some Exact Solitary Wave Solutions

Master's Thesis from the year 2021 in the subject Mathematics - Applied Mathematics, grade: 99/110, University of Verona, language: English, abstract: The current study deals with distinct kinds of solitary wave solutions for the fractional generalized Duffing model and fractional diffusion reaction model with novel truncated M-fractional derivative. We are also interested in studying some special cases of the fractional generalized Duffing model. These are known as fractional Landau-Ginzburg-Higgs equation, classical fractional Klein-Gordon equation, the Phi-4 equation, the Sine-Gordon equation and the Duffing equation. The obtained results can be used in describing these models in some better way. The novel fractional derivative operator namely M-fractional derivative is used to study the above-mentioned models. Also, the obtained results are verified via symbolic software Mathematica. A modified integration method, the extended Sinh-Gordon equation expansion method (EShGEEM) is employed to secure the aforesaid solitary wave solutions. Furthermore, the obtained results show that the suggested approach have broadened capacity to obtain the different wave solutions of the fractional differential equations effectively. At the end, the results are also explained through their graphical representations.