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Title:	Solution schemes for two-mode and fractional nonlinear partial differential equations
Authors:	Ali Mahmoud Mohammad Jaradat (P70776)
Supervisor:	Mohd Salmi Md Noorani, Prof. Dr.
Keywords:	Differential equations Nonlinear Universiti Kebangsaan Malaysia -- Dissertations Dissertations, Academic -- Malaysia
Issue Date:	8-Feb-2019
Description:	In this thesis, we aim to study two different topics in the field of partial differential equations. First, we consider time-fractional partial differential equations where the fractional derivative considered in this study is of Caputo's type. We presented a scheme based on the generalization of Taylor power series to provide an analytical solution of such problems. The residual power series method will be applied for the first time to extract approximate solutions of three fractional models: They are the Caputo-time-fractional Wu-Zhang system, the Caputo-time-fractional Belousov-Zhabotinsky system and Caputo-time-fractional combined KdV and mKdV equations. Graphical justifications on the reliability of the proposed method are provided. Also, the effects of the fractional order on the solution of these models are also discussed. The second aim, we construct new types of nonlinear equations called two-mode equations. These models describe the propagation of two different wave modes simultaneously. In this work, we establish for the first time the following two-mode nonlinear partial differential equations: (1 + 1)-dimensional two-mode higher-order Boussinesq-Burger system and (1 + 1)-dimensional two-mode mKdV equation. Also, we generalized the (1+1)-dimensional two-mode nonlinear partial differential equation to (n + 1)-dimensional two-mode nonlinear partial differential equation for any first order (n+1)- dimensional nonlinear partial differential equations in time and we found the (2 + 1)-dimensional two-mode Gardner equation, (3 + 1)-dimensional two-mode Gardner equation, (3 + 1)-dimensional KdV equation. And we used the simplified bilinear method to find the necessary constraint conditions that guarantee the existence of both regular and singular multiple soliton solutions of the above two-mode equations and systems. Also, the hyperbolic-tangent expansion method is used as an alternative technique to extract more solutions., Certification of Master's/Doctoral Thesis is not available,Ph.D.
Pages:	110
Publisher:	UKM, Bangi
Appears in Collections:	Faculty of Science and Technology / Fakulti Sains dan Teknologi

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