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Oscillation of impulsive conformable fractional differential equations

100%
Tariboon J., Ntouyas S. K.
Open Mathematics
|
2016
|
tom 14
|
nr 1
497-508
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.
2
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Positive solutions for Hadamard differential systems with fractional integral conditions on an unbounded domain

81%
Jessada T., Ntouyas S. K., Asawasamrit S., Promsakon C.
Open Mathematics
|
2017
|
tom 15
|
nr 1
645-666
EN
In this paper, we investigate the existence of positive solutions for Hadamard type fractional differential system with coupled nonlocal fractional integral boundary conditions on an infinite domain. Our analysis relies on Guo-Krasnoselskii’s and Leggett-Williams fixed point theorems. The obtained results are well illustrated with the aid of examples.
3
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System of fractional differential equations with Erdélyi-Kober fractional integral conditions

81%
Thongsalee N., Laoprasittichok S., Ntouyas S. K., Tariboon J.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
In this paper we study existence and uniqueness of solutions for a system consisting from fractional differential equations of Riemann-Liouville type subject to nonlocal Erdélyi-Kober fractional integral conditions. The existence and uniqueness of solutions is established by Banach’s contraction principle, while the existence of solutions is derived by using Leray-Schauder’s alternative. Examples illustrating our results are also presented.
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