Analytical solutions for multi-term time-space coupling fractional delay partial differential equations with mixed boundary conditions

作者：Ding, Xiao-Li^*; Jiang, Yao-Lin

来源：Communications in Nonlinear Science & Numerical Simulation, 2018, 65: 231-247.

DOI：10.1016/j.cnsns.2018.05.022

• Coupling fractional delay partial differential equations
• Mixed Robin boundary condition
• Spectral representation
• Integral transform
• Analytical solution

In this paper, we consider the analytical solutions of multi-term time-space coupling fractional delay partial differential equations for general mixed Robin boundary conditions on a finite domain. Firstly, integral transforms and method of reduction to integral equations are used to obtain the analytical solutions of multi-term time coupling delay fractional differential equations. Then, the technique of spectral representation of the fractional Laplacian operator is used to convert the multi-term time-space coupling fractional delay partial differential equations to the multi-term time coupling fractional delay differential equations. By applying the obtained analytical solutions to the resulting multi-term time coupling fractional delay differential equations, the desired analytical solutions of the multiterm time-space coupling fractional delay partial differential equations are given. Our results are applied to derive the analytical solutions of some special cases to demonstrate their applicability.

• 出版日期2018-12
• 单位西安交通大学; 西安工程大学