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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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Existence results for q-difference inclusions with three-point boundary conditions involving different numbers of q

81%
Ntouyas S., Sitthiwirattham T., Tariboon J.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2014
|
tom 34
|
nr 1
41-59
EN
In this paper, we study a new class of three-point boundary value problems of nonlinear second-order q-difference inclusions. Our problems contain different numbers of q in derivatives and integrals. By using fixed point theorems, some new existence results are obtained in the cases when the right-hand side has convex as well as noncovex values.
3
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Hybrid fractional integro-differential inclusions

81%
Ntouyas S., Laoprasittichok S., Tariboon J.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2015
|
tom 35
|
nr 2
151-164
EN
In this paper we study an existence result for initial value problems for hybrid fractional integro-differential inclusions. A hybrid fixed point theorem for a sum of three operators due to Dhage is used. An example illustrating the obtained result is also presented.
4
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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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