Year 2019, Volume 7, Issue 1, Pages 203 - 207 2019-04-15

Oscillation Criteria for Higher Order Fractional Differential Equations with Mixed Nonlinearities

Tuğba Yalçın Uzun [1] , Hande Büyükçavuşoğlu Erçolak [2] , Mustafa Kemal Yıldız [3]

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In this article, we consider higher order fractional nonlinear differential equation of type \begin{align*} &_aD_t^qx(t)-p(t)x(t)+\sum_{i=1}^m q_i(t)|x(t)|^{\lambda_i-1}x(t)=v(t)\notag\\ &\underset{t\rightarrow a^+}{\lim}J_a^{n-q}x(t)=a_n\\ &_aD_t^{q-k}x(a)=a_k, \quad\quad\ k=1,...,n-1\notag \end{align*} where $_aD_t^q$is Riemann-Liouville fractional differential operator of order $q$, $m-1<q\leq m, m\geq1$ is an integer. We obtain some oscillation criteria for this equation.

fractional differential equations, Oscillation
  • [1] Shao, J., Zheng, Z. and Meng, F. Oscillation criteria for higher order fractional differential equations with mixed nonlinearities, Advanced in Difference Equations 2013:323 (2013)
  • [2] Chen,D. X., Qu, P. X. and Lan, Y. H., Forced oscillation of certain fractional differantial equations, Advanced in Difference Equations 2013:125 (2013)
  • [3] Grace, S. R., Agarwal, R. P., Wong, P. J.Y. and Zafer, A. On the oscillation of fractional differential equations, An International Journal for Theory and Applications Vol:15, No:2 (2012)
  • [4] Diethelm, K. The Analysis of Fractional Differential Equations, Springer, Berlin(2010)
Primary Language en
Subjects Engineering
Journal Section Articles
Authors

Author: Tuğba Yalçın Uzun (Primary Author)
Institution: AFYON KOCATEPE ÜNİVERSİTESİ
Country: Turkey


Author: Hande Büyükçavuşoğlu Erçolak
Institution: AFYON KOCATEPE ÜNİVERSİTESİ
Country: Turkey


Author: Mustafa Kemal Yıldız
Institution: AFYON KOCATEPE ÜNİVERSİTESİ
Country: Turkey


Dates

Publication Date: April 15, 2019

Bibtex @conference paper { konuralpjournalmath369895, journal = {Konuralp Journal of Mathematics (KJM)}, issn = {}, eissn = {2147-625X}, address = {Mehmet Zeki SARIKAYA}, year = {2019}, volume = {7}, pages = {203 - 207}, doi = {}, title = {Oscillation Criteria for Higher Order Fractional Differential Equations with Mixed Nonlinearities}, key = {cite}, author = {Yalçın Uzun, Tuğba and Büyükçavuşoğlu Erçolak, Hande and Yıldız, Mustafa Kemal} }
APA Yalçın Uzun, T , Büyükçavuşoğlu Erçolak, H , Yıldız, M . (2019). Oscillation Criteria for Higher Order Fractional Differential Equations with Mixed Nonlinearities. Konuralp Journal of Mathematics (KJM), 7 (1), 203-207. Retrieved from http://dergipark.org.tr/konuralpjournalmath/issue/31492/369895
MLA Yalçın Uzun, T , Büyükçavuşoğlu Erçolak, H , Yıldız, M . "Oscillation Criteria for Higher Order Fractional Differential Equations with Mixed Nonlinearities". Konuralp Journal of Mathematics (KJM) 7 (2019): 203-207 <http://dergipark.org.tr/konuralpjournalmath/issue/31492/369895>
Chicago Yalçın Uzun, T , Büyükçavuşoğlu Erçolak, H , Yıldız, M . "Oscillation Criteria for Higher Order Fractional Differential Equations with Mixed Nonlinearities". Konuralp Journal of Mathematics (KJM) 7 (2019): 203-207
RIS TY - JOUR T1 - Oscillation Criteria for Higher Order Fractional Differential Equations with Mixed Nonlinearities AU - Tuğba Yalçın Uzun , Hande Büyükçavuşoğlu Erçolak , Mustafa Kemal Yıldız Y1 - 2019 PY - 2019 N1 - DO - T2 - Konuralp Journal of Mathematics (KJM) JF - Journal JO - JOR SP - 203 EP - 207 VL - 7 IS - 1 SN - -2147-625X M3 - UR - Y2 - 2019 ER -
EndNote %0 Konuralp Journal of Mathematics (KJM) Oscillation Criteria for Higher Order Fractional Differential Equations with Mixed Nonlinearities %A Tuğba Yalçın Uzun , Hande Büyükçavuşoğlu Erçolak , Mustafa Kemal Yıldız %T Oscillation Criteria for Higher Order Fractional Differential Equations with Mixed Nonlinearities %D 2019 %J Konuralp Journal of Mathematics (KJM) %P -2147-625X %V 7 %N 1 %R %U
ISNAD Yalçın Uzun, Tuğba , Büyükçavuşoğlu Erçolak, Hande , Yıldız, Mustafa Kemal . "Oscillation Criteria for Higher Order Fractional Differential Equations with Mixed Nonlinearities". Konuralp Journal of Mathematics (KJM) 7 / 1 (April 2019): 203-207.
AMA Yalçın Uzun T , Büyükçavuşoğlu Erçolak H , Yıldız M . Oscillation Criteria for Higher Order Fractional Differential Equations with Mixed Nonlinearities. Konuralp J. Math.. 2019; 7(1): 203-207.
Vancouver Yalçın Uzun T , Büyükçavuşoğlu Erçolak H , Yıldız M . Oscillation Criteria for Higher Order Fractional Differential Equations with Mixed Nonlinearities. Konuralp Journal of Mathematics (KJM). 2019; 7(1): 207-203.