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

摘要

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. (c) 2018 Published by Elsevier B.V.