Oscillation properties for solutions of a kind of partial fractional differential equations with damping term

Volume 9, Issue 4, pp 1600--1608 http://dx.doi.org/10.22436/jnsa.009.04.17

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1504 Downloads
• 2550 Views

Authors

Wei Nian Li - Department of Mathematics, Binzhou University, Shandong 256603, P. R. China. Weihong Sheng - Department of Mathematics, Binzhou University, Shandong 256603, P. R. China.

Abstract

The aim of the present paper is to obtain sufficient conditions for oscillation of solutions of partial fractional differential equations with the damping term of the form \[D^{1+\alpha}_{+;t} u(x; t) + p(t)D^\alpha _{+;t} u(x; t) = a(t)\Delta u(x; t) + \Sigma^m_{i=1} a_i(t)\Delta u(x; t - \tau_i) - q(x; t) \int^t_0 (t - \xi)^{-\alpha} u(x; \xi)d\xi; \quad (x; t) \in \Omega\times \mathbb{R}_+ \equiv G.\] Two examples are given to illustrate the main results.

Share and Cite

Keywords

• Oscillation
• fractional partial differential equation
• Riemann-Liouville derivative
• damping term.

MSC

•  35B05
•  35R11
•  26A33

References

• [1] S. Abbas, M. Benchohra, G. M. N'Guérékata, Topics in Fractional Differential Equations, Springer, New York (2012)


• [2] C. Chen, Y. L. Jiang, Lie group analysis method for two classes of fractional partial differential equations, Commun. Nonlinear Sci. Numer. Simul., 26 (2015), 24-35.


• [3] R. Courant, D. Hilbert, Methods of Mathematical Physics, Interscience, New York (1966)


• [4] S. Das, Functional Fractional Calculus for System Identification and Controls, Springer, Berlin (2008)


• [5] S. Harikrishnan, P. Prakash, J. J. Nieto , Forced oscillation of solutions of a nonlinear fractional partial differential equation, Appl. Math. Comput., 254 (2015), 14-19.


• [6] H. Jafari, M. Nazari, D. Baleanu, C. M. Khalique, A new approach for solving a system of fractional partial differential equations, Comput. Math. Appl., 66 (2013), 838-843.


• [7] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science B. V., Amsterdam (2006)


• [8] W. N. Li , Forced oscillation criteria for a class of fractional partial differential equations with damping term, Math. Probl. Eng., 2015 (2015), 6 pages.


• [9] I. Podlubny, Fractional Differential Equations, Academic Press Inc., San Diego (1999)


• [10] P. Prakash, S. Harikrishnan, M. Benchohra, Oscillation of certain nonlinear fractional partial differential equation with damping term, Appl. Math. Lett., 43 (2015), 72-79.


• [11] P. Prakash, S. Harikrishnan, J. J. Nieto, J. H. Kim, Oscillation of a time fractional partial differential equation, Electron, J. Qual. Theory Differ. Equ., 2014 (2014), 10 pages.


• [12] B. Zheng , Exact solutions for some fractional partial differential equations by the \((G' / G)\) method, Math. Probl. Eng., 2013 (2013), 13 pages.


• [13] B. Zheng, Q. Feng, A new approach for solving fractional partial differential equations in the sense of the modified Riemann-Liouville derivative, Math. Probl. Eng., 2014 (2014), 7 pages.


• [14] Y. Zhou, Basic Theory of Fractional Differential Equations, World Scientific Publishing Co. Pte. Ltd., Hackensack (2014)