Oscillation of impulsive conformable fractional differential equations

• Autorzy: Jessada Tariboon , Sotiris K. Ntouyas
• Języki publikacji: EN

Abstrakty

EN

In this paper, we investigate oscillation results for the solutions of impulsive conformable fractional differential equations of the form tkDαpttkDαxt+rtxt+qtxt=0,t≥t0,t≠tk,xtk+=akx(tk−),tkDαxtk+=bktk−1Dαx(tk−),k=1,2,…. $$\left\{ \begin{array}{l} {t_k}{D^\alpha }\left( {p\left( t \right)\left[ {{t_k}{D^\alpha }x\left( t \right) + r\left( t \right)x\left( t \right)} \right]} \right) + q\left( t \right)x\left( t \right) = 0,\quad t \ge {t_0},\;t \ne {t_k},\\ x\left( {t_k^ + } \right) = {a_k}x(t_k^ - ),\quad {t_k}{D^\alpha }x\left( {t_k^ + } \right) = {b_{k\;{t_{k - 1}}}}{D^\alpha }x(t_k^ - ),\quad \;k = 1,2, \ldots. \end{array} \right.$$ Some new oscillation results are obtained by using the equivalence transformation and the associated Riccati techniques.

Słowa kluczowe

EN

Fractional differential equations; Impulsive differential equations; Conformable fractional derivative; Oscillation

Kategorie tematyczne

• 34A08: Fractional differential equations
• 34C10: Oscillation theory, zeros, disconjugacy and comparison theory
• 34A37: Differential equations with impulses

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2016
• Tom: 14
• Numer: 1
• Strony: 497-508

Daty

wydano

2016-01-01

otrzymano

2016-05-24

zaakceptowano

2016-06-21

online

2016-07-22

Twórcy

autor

Jessada Tariboon

• Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800,

autor

Sotiris K. Ntouyas

• Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece and Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589,

Identyfikatory

DOI

10.1515/math-2016-0044