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Analytical solutions for multi-term time-space fractional partial differential equations with nonlocal damping terms

Xiao-Li Ding EMAIL logo and Juan J. Nieto


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


The work of the X.L. Ding was supported by the Natural Science Foundation of China (11501436) and Young Talent fund of University Association for Science and Technology in Shaanxi, China (20170701). The work of J.J. Nieto has been partially supported by the AEI of Spain under Grant MTM2016-75140-P and co-financed by European Community fund FEDER, and XUNTA de Galicia under grants GRC2015-004 and R2016/022. The authors are grateful to Prof. Virginia Kiryakova for the useful comments and relevant references.


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Received: 2017-5-11
Published Online: 2018-6-9
Published in Print: 2018-4-25

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