A new analytical modelling for nonlocal generalized Riesz fractional sine-Gordon equation

详细信息    查看全文

• 作者：S. Saha Ray ^{santanusaharay@yahoo.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Modified decomposition method with Fourier transform (MDM-FT) ; Riesz space fractional derivative ; Nonlocal sine-Gordon equation ; Hurwitz zeta function ; Riemann zeta function ; Generalized zeta function
• 刊名：Journal of King Saud University - Science
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：28
• 期：1
• 页码：48-54
• 全文大小：1362 K

文摘

In this paper, a novel approach comprising the modified decomposition method with Fourier transform has been implemented for the approximate solution of fractional sine-Gordon equation $u_{\mathit{tt}}-{}^R{D}_x^{\alpha }u+\sin u=0$ where ${}^R{D}_x^{\alpha }$ is the Riesz space fractional derivative, 1≤α≤2$1\le \alpha \le 2$. For α = 2, it becomes classical sine-Gordon equation u_tt − u_xx + sin u = 0 and corresponding to α = 1, it becomes nonlocal sine-Gordon equation u_tt − Hu + sin u = 0 which arises in Josephson junction theory, where H is the Hilbert transform. The fractional sine-Gordon equation is considered as an interpolation between the classical sine-Gordon equation (corresponding to α = 2) and nonlocal sine-Gordon equation (corresponding to α = 1). Here the analytic solution of fractional sine-Gordon equation is derived by using the modified decomposition method with Fourier transform. Then, we analyze the results by numerical simulations, which demonstrate the simplicity and effectiveness of the present method.