On solvability of fractional coupled hybrid systems
type: Item
instance of: scholarly article
title: On solvability of fractional coupled hybrid systems
zbMATH Open document ID: 1354.34016
author: Yousef Gholami
author: K. Ghanbari
published in: Asia Pacific Journal of Mathematics
publication date: 2016-10-12T00:00:00Z
full work available at URL: 2-1-54-68.pdf
review text: From the introduction and summary: \[ \begin{aligned} \lambda_1 D^\alpha_{0^+}(u(t)-f(t,u(t)))-\lambda_2 u(t)= g_1(t,u(t), v(t)),\quad & 1<\alpha\leq 2,\\ \mu_1 D^\beta_{0^+}(v(t)-f(t,v(t)))-\mu_2 v(t)= g_2(t, u(t),v(t)),\quad & 1<\beta\leq 2,\end{aligned} \] \[ \begin{aligned} u(0)-f*0,u(0))= \gamma_1(u(1)-\lambda_1 f(1,u(1))),\quad & u'(0)= f'(0, u(0))),\\ v(0)-f(0, v(0))= \gamma_1(v(1)-\mu_1 f(1,v(1))),\quad & v'(0)= f'(0,v(0)),\end{aligned} \] where \(t\in{\mathcal I}= (0,1)\) and \(D^\alpha_{0^+}\) denotes the fractional Caputo derivative of order \(\alpha>0\). Additionally assume that \(\lambda_i,\mu_i\in \mathbb{R}^+\), \(\gamma_i\in (0,1/2\delta)\) for \(i= 1,2\), where \(\delta\) is an upper bound for the generalized Mittag-Leffler function \(E_{\alpha,1}(t)\). We study the existence of multiple positive solutions. To this aim we apply fixed point theorems.
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B18
zbMATH DE Number: 6637973
zbMATH Keywords: fractional derivatives and integrals
zbMATH Keywords: fixed point theorem
zbMATH Keywords: positive solutions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6637973