The extremal iteration solution to a coupled system of nonlinear conformable fractional differential equations
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Authors
Suli Liu
- Department of Mathematics, Jilin University, Changchun 130012, P. R. China.
- Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, T6G 2G1, Canada.
Han Wang
- Department of Mathematics, Jilin University, Changchun 130012, P. R. China.
Xiaoping Li
- Institute of Mathematics and Finance, Xiangnan University, Chenzhou 423000, P. R. China.
Huilai Li
- Department of Mathematics, Jilin University, Changchun 130012, P. R. China.
Abstract
In this paper, we consider a coupled system of nonlinear conformable fractional differential equations by using the comparison principle and the monotone iterative technique combined with the method of upper and lower solutions:
\[
\left\{\begin{aligned}
x^{(\alpha)}(t)=f(t,x(t),y(t)), t\in[a,b],\\
y^{(\alpha)}(t)=g(t,y(t),x(t)), t\in[a,b],\\
x(a)=x_0^*,\quad y(a)=y_0^*,
\end{aligned}
\right.
\]
where \(f,\,g\in C([a,b]\times\mathbb{R}\times\mathbb{R},\mathbb{R}),\ x_0^*,\,y_0^*\in\mathbb{R},\ x_0^*\le y_0^*,
\ x^{(\alpha)},\,y^{(\alpha)}\) are the conformable fractional derivatives with \(0<\alpha\le 1\).
We obtain the existence of extremal iteration solution to the system,
and the main results are examined by the help of an example.
Share and Cite
ISRP Style
Suli Liu, Han Wang, Xiaoping Li, Huilai Li, The extremal iteration solution to a coupled system of nonlinear conformable fractional differential equations, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 9, 5082--5089
AMA Style
Liu Suli, Wang Han, Li Xiaoping, Li Huilai, The extremal iteration solution to a coupled system of nonlinear conformable fractional differential equations. J. Nonlinear Sci. Appl. (2017); 10(9):5082--5089
Chicago/Turabian Style
Liu, Suli, Wang, Han, Li, Xiaoping, Li, Huilai. "The extremal iteration solution to a coupled system of nonlinear conformable fractional differential equations." Journal of Nonlinear Sciences and Applications, 10, no. 9 (2017): 5082--5089
Keywords
- Nonlinear conformable fractional differential equations
- extremal system of solutions
- monotone iterative method
- comparison principle
- upper and lower solutions
MSC
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