Existence results to positive solutions of fractional BVP with $${\varvec{}}$$-derivatives |
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Authors: | Rahmat Darzi Bahram Agheli |
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Institution: | 1.Department of Mathematics, Neka Branch,Islamic Azad University,Neka,Iran;2.Department of Mathematics, Qaemshahr Branch,Islamic Azad University,Qaemshahr,Iran |
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Abstract: | This paper investigates the existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem with fractional q-derivative $$\begin{aligned}&D_{q}^{\alpha }u(t)+f(t,u(t))=0, \quad {0<t<1, ~3<\alpha \le 4,} \\&u(0)= D_{q}u(0)=D_{q}^{2}u(0)=0, \quad D_{q}^{2}u(1)=\beta D_{q}^{2}u(\eta ), \end{aligned}$$ where \(D_{q}^{\alpha }\) denotes the Riemann–Liouville q-derivative of order \(\alpha \), \(0<\eta <1\) and \(1-\beta \eta ^{\alpha -3}>0\). Our analysis relies a fixed point theorem in partially ordered sets. An example to illustrate our results is given. |
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