**Volume 10, Issue 4, pp 1345--1349**

**Publication Date**: 2017-04-20

**Jiao-Lian Zhao**
- Department of Mathematics and Physics, Weinan Normal University, Weinan City, Shaanxi Province, 714009, China.

**Jing-Lin Wang**
- Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin City, 300160, China.

**Feng Qi**
- Institute of Mathematics, Henan Polytechnic University, Jiaozuo City, Henan Province, 454010, China.

In the paper, the authors find a simple and significant expression in terms of the Stirling numbers for derivative polynomials of a function with a parameter related to the higher order Apostol-Euler numbers and to the higher order Frobenius-Euler numbers. Moreover, the authors also present a common solution to a sequence of nonlinear ordinary differential equations.

Derivative polynomial, Stirling number, nonlinear ordinary differential equation, solution.

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