@Article{JNMA-4-454,
author = {Bai , Zhanbing and Shi , Dongmei},
title = {Triple Positive Solutions for a Class of Fractional Boundary Value Problem System},
journal = {Journal of Nonlinear Modeling and Analysis},
year = {2022},
volume = {4},
number = {3},
pages = {454--464},
abstract = {<p style="text-align: justify;">In this paper, the solvability for the following fractional boundary
value problem system $$^CD^{σ_1}_{0+}v_1(t) = f_1(t, v_2(t), D^{\mu_1}_{0+}v_2(t)), \ 0 &lt; t &lt; 1,$$ $$^CD^{σ_2}_{0+}v_2(t) = f_2(t, v_1(t), D^{\mu_2}_{0+}v_1(t)), \ 0 &lt; t &lt; 1,$$ $$v_1&#39; (0) = bv_1(0), \ v_1&#39;&#39;(0) = 0, \ ^CD^{θ_1}_{0+}v_1(1) = a · ^C D^{θ_2} _{0+}v_1(η),$$ $$v_2&#39;(0) = bv_2(0), \ v_2&#39;&#39;(0) = 0, \ ^CD^{θ_1}_{0+}v_2(1) = a · ^CD^{θ_2}_{0+}v_2(η),$$ is studied, where $a &gt; 0,$ $−1 &lt; b &lt; 0,$ $2 &lt; σ_1, σ_2 ≤ 3,$ $0 &lt; η &lt; 1,$ $0 &lt; \mu_1, \mu_2 ≤ 1,$ $0 &lt; θ_2 ≤ θ_1 ≤ 1,$ $f_1, f_2:$ $[0, 1] × \mathbb{R}^+ \times \mathbb{R} → \mathbb{R}^+$ are continuous, $^CD^{σ_1} _{0+}v_1(t),$ $^CD^{σ_2}_{0+}v_2(t)$ are the Caputo fractional derivatives, and $D^{\mu_1}_{0+}v_2(t),$ $D^{\mu_2}_{0+}v_1(t)$ are
the Riemann-Liouville fractional derivatives. The fixed point theorem is used
to prove that there are three positive solutions to problems.</p>},
issn = {2562-2862},
doi = {https://doi.org/10.12150/jnma.2022.454},
url = {http://global-sci.org/intro/article_detail/jnma/20717.html}
}