1
Department of Mathematics, Neka Branch, Islamic Azad University, Neka, Iran
2
Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
Abstract
In this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form $D_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0<t<1, 2<alpha<3, x(0)= x'(0)=0, x'(1)=beta x(xi)$, where $D_{0^{+}}^{alpha}$ denotes the standard Riemann-Liouville fractional derivative,$0<xi<1$ and $0<\beta\xi^{\alpha-1}<\alpha-1$ Our analysis relies a fixed point theorem in partially ordered sets. An illustrative example is also presented.
Darzi, R., Agheli, B. (2015). Existence and uniqueness of positive and nondecreasing solution for nonlocal fractional boundary value problem. Computational Methods for Differential Equations, 3(2), 123-133.
MLA
Rahmat Darzi; Bahram Agheli. "Existence and uniqueness of positive and nondecreasing solution for nonlocal fractional boundary value problem". Computational Methods for Differential Equations, 3, 2, 2015, 123-133.
HARVARD
Darzi, R., Agheli, B. (2015). 'Existence and uniqueness of positive and nondecreasing solution for nonlocal fractional boundary value problem', Computational Methods for Differential Equations, 3(2), pp. 123-133.
VANCOUVER
Darzi, R., Agheli, B. Existence and uniqueness of positive and nondecreasing solution for nonlocal fractional boundary value problem. Computational Methods for Differential Equations, 2015; 3(2): 123-133.
)
