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This article is cited in 1 scientific paper (total in 1 paper)
Fractional boundary value problem on the half-line
Bilel Khamessiab a Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawwarah, Saudi-Arabia
b Université Tunis El Manar, Faculté des sciences de Tunis, LR18ES09 Modélisation mathématique, analyse harmonique et théorie du potentiel, 2092 Tunis, Tunisia
Abstract:
We consider the semilinear fractional boundary value problem \begin{equation*} D^{\beta}\left(\frac{1}{b(x)}D^{\alpha}u\right)=a(x)u^{\sigma} \text{in } (0,\infty) \end{equation*} with the conditions $\lim_{x\rightarrow 0} x^{2-\beta} \frac{1}{b(x)}D^{\alpha}u(x) =\lim_{x\rightarrow \infty} x^{1-\beta}\frac{1}{b(x)}D^{\alpha}u(x)=0$ and $\lim_{x\rightarrow 0} x^{2-\alpha}u(x)= \lim_{x\rightarrow \infty} x^{1-\alpha}u(x)=0$, where $\beta,\alpha \in (1,2)$, $\sigma\in(-1,1)$ and $D^{\beta}, D^{\alpha}$ stand for the standard Riemann–Liouville fractional derivatives. The functions $ a,b : (0,\infty)\rightarrow \mathbb{R}$ are nonnegative continuous functions satisfying some appropriate conditions. The existence and the uniqueness of a positive solution are established. Also, a description of the global behavior of this solution is given.
Key words and phrases:
fractional differential equation, positive solution, Schauder fixed point theorem.
Received: 07.05.2019 Revised: 14.10.2019
Citation:
Bilel Khamessi, “Fractional boundary value problem on the half-line”, Zh. Mat. Fiz. Anal. Geom., 16:1 (2020), 27–45
Linking options:
https://www.mathnet.ru/eng/jmag745 https://www.mathnet.ru/eng/jmag/v16/i1/p27
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Abstract page: | 64 | Full-text PDF : | 42 | References: | 14 |
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