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In this paper, the complete discrimination system method is used to construct the single traveling wave solutions for the (3+1)-dimensional Jimbo-Miwa equations with space-time fractional derivative. As a result, we get the exact traveling wave solutions of the (3+1)-dimensional Jimbo-Miwa equation with space-time fractional derivative, which include rational function solutions, Jacobian elliptic function solutions, hyperbolic function solutions, and trigonometric function solutions. Some graphical representations of the solutions are also provided. Finally, the obtained solution is compared with the existing literature.

By means of the mathematical analysis theory, inequality theory, mathematical induction and the dimension reduction method, under the proper hypotheses, we establish the following cyclic inequalities: \[\sum_{i=1}^{n} {a_i^{{a_{n+1-i}}}}\leq\sum_{\text{cyc}:~n}^{1\leq i\leq n} {a_i^{{a_{i + 1}}}}\leq \sum_{i=1}^{n} {a_i^{{a_i}}},~\forall n\geq2.\], Comment: 13 pages