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Existence and uniqueness of positive and nondecreasing solution for nonlocal fractional boundary value problem | ||
| Computational Methods for Differential Equations | ||
| مقاله 5، دوره 3، شماره 2، تیر 2015، صفحه 123-133 اصل مقاله (161.26 K) | ||
| نوع مقاله: Research Paper | ||
| نویسندگان | ||
| Rahmat Darzi1؛ Bahram Agheli* 2 | ||
| 1Department of Mathematics, Neka Branch, Islamic Azad University, Neka, Iran | ||
| 2Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Boundary value problem؛ fixed point theorem؛ Partially ordered set؛ Positive solution؛ nondecreasing solution | ||
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