Existence of nontrivial solutions for a system of fractional advection–dispersion equations

Original Paper


In this paper, we investigate the existence of nontrivial solutions for a class of fractional advection–dispersion systems. The approach is based on the variational method by introducing a suitable fractional derivative Sobolev space. We take two examples to demonstrate the main results.


Fractional advection–dispersion equation Weak solution Critical point theory Anomalous diffusion Variational method 

Mathematics Subject Classification

58E05 34B15 26A33 



Lishan Liu was supported financially by the National Natural Science Foundation of China (11371221). Dexiang Ma was supported financially by the Fundamental Research Funds for the Central Universities (2014MS62).


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Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsNorth China Electric Power UniversityBeijingChina
  2. 2.School of Mathematical SciencesQufu Normal UniversityQufuChina
  3. 3.Department of Mathematics and StatisticsCurtin UniversityPerthAustralia

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