Analytical solutions for coupling fractional partial differential equations with Dirichlet boundary conditions

作者：Ding, Xiao-Li^*; Nieto, Juan J.

来源：Communications in Nonlinear Science & Numerical Simulation, 2017, 52: 165-176.

DOI：10.1016/j.cnsns.2017.04.020

• Coupling fractional partial differential equations
• Dirichlet boundary condition
• Fractional Laplacian operator
• Spectral representation
• Analytical solution

In this paper, we consider the analytical solutions of coupling fractional partial differential equations (FPDEs) with Dirichlet boundary conditions on a finite domain. Firstly, the method of successive approximations is used to obtain the analytical solutions of coupling multi-term time fractional ordinary differential equations. Then, the technique of spectral representation of the fractional Laplacian operator is used to convert the coupling FPDEs to the coupling multi-term time fractional ordinary differential equations. By applying the obtained analytical solutions to the resulting multi-term time fractional ordinary differential equations, the desired analytical solutions of the coupling FPDEs are given. Our results are applied to derive the analytical solutions of some special cases to demonstrate their applicability.

• 出版日期2017-11
• 单位西安工程大学