一类带有阻尼项的非线性分数阶偏微分方程解的振动性
Oscillation of Nonlinear Fractional Partial Differential Equation with Damping

DOI: 10.12677/PM.2016.63023, PP. 157-161

Keywords: 振动，分数阶偏微分方程，改进的黎曼–刘维尔分数阶导
Oscillation, Fractional Partial Differential Equations, Modified Riemann-Liouville Derivative

Full-Text   Cite this paper   Add to My Lib

Abstract:

本文将对一类带有阻尼项和时滞项的非线性分数阶偏微分方程进行研究，研究条件为第二类边界条件，研究方法为利用改进的黎曼–刘维尔分数阶定义下的相关性质和黎卡提变换。得到的相关结论将给出相关例子作为进一步说明。
In this paper, we will investigate oscillation of nonlinear fractional partial differential equation with damping and several delays subject to Neumann boundary condition by using the properties of the modified Riemann-Liouville derivative as well as Riccati transformation. The main results are illustrated by examples.

References

[1]	Chen, D.X., Qu, P.X. and Lan, Y.H. (2013) Forced Oscillation of Certain Fractional Differential Equations. Advances in Difference Equations, 2013, 1-10.
[2]	Yang, J.C., Liu, A.P. and Liu, T. (2015) Forced Oscillation of Nonlinear Fractional Differential Equations with Damping Term. Advances in Difference Equations, 2015, 1-7. http://dx.doi.org/10.1186/s13662-014-0331-4
[3]	Li, W.N. (2015) Forced Oscillation Criteria for a Class of Fractional Partial Differential Equations with Damping Term. Mathematical Problems in Engineering, 2015, 1-7.
[4]	Qin, H.Z. and Zheng, B. (2013) Oscillation of a Class of Fractional Differential Equations with Damping Term. The Scientific World Journal, 2013, 1-9.
[5]	Prakash, P., Harikrishnan, S., Nieto, J.J. and Kim, J.-H. (2014) Oscillation of a Time Fractional Partial Differential Equation. Electronic Journal of Qualitative Theory of Differential Equations, 15, 1-10. http://dx.doi.org/10.14232/ejqtde.2014.1.15
[6]	Harikrishnan, S., Prakash, P. and Nieto, J.J. (2015) Forced Os-cillation of Solutions of a Nonlinearfractional Partial Differential Equation. Applied Mathematics and Computation, 254, 14-19. http://dx.doi.org/10.1016/j.amc.2014.12.074
[7]	Prakash, P., Harikrishnan, S. and Benchohra, M. (2015) Oscillation of Certain Nonlinear Fractional Partial Differential Equation with Damping Term. Applied Mathematics Letters, 43, 72-79. http://dx.doi.org/10.1016/j.aml.2014.11.018
[8]	Li, W.N. (2015) On the Forced Oscillation of Certain Fractional Partial Differential Equations. Applied Mathematics Letters, 2015, 5-9. http://dx.doi.org/10.1016/j.aml.2015.05.016

Full-Text