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

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 multi-term 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.