Existence of solutions for a system of fractional differential equations with coupled nonlocal boundary conditions
type: Item
instance of: scholarly article
title: Existence of solutions for a system of fractional differential equations with coupled nonlocal boundary conditions
zbMATH Open document ID: 1401.34006
author: Bashir Ahmad
author: Rodica Luca
publication date: 2018-10-19T00:00:00Z
review text: The authors consider the following system of nonlinear fractional differential equations \[ \begin{aligned} ^{c}D^{\alpha}_{0+}u(t)&=f(t,v(t),^{c}D^p_{0+}v(t)),\;t\in (0,1),\;\alpha\in (n-1,n],\;p\in (0,1),\\ ^{c}D^{\beta}_{0+}v(t)&=g(t,u(t),^{c}D^q_{0+}u(t)),\;t\in (0,1),\;\beta\in (m-1,m],\;q\in (0,1),\end{aligned} \] with solutions subjected to the coupled nonlocal integral boundary conditions \[ \begin{aligned} u(0)&=\phi(v),\;u'(0)=0, \ldots, u^{(n-2)}(0)=0, u(1)=\lambda I^{\gamma}_{0+}v(\xi),\;\xi\in (0,1),\\ v(0)&=\psi(v),\;v'(0)=0, \ldots, v^{(m-2)}(0)=0, v(1)=\mu I^{\delta}_{0+}u(\eta),\;\eta\in (0,1),\end{aligned} \] where \(^{c}D^{\chi}_{0+}\) denotes the Caputo fractional derivative of order \(\chi\), \(I^{\kappa}_{0+}\) denotes the Riemann-Liouville fractional integral of order \(\kappa,\) \(f,g: [0,1]\times {\mathbb R}\times {\mathbb R}\to {\mathbb R}\), \(\phi, \psi: C([0,1],{\mathbb R})\to \mathbb R\) are continuous functions and \(\lambda, \mu \in \mathbb R\). Existence results are obtained by using the Schauder fixed point theorem and the nonlinear alternative of Leray-Schauder type. Examples illustrating the obtained results are also presented.
reviewed by: Sotiris K. Ntouyas
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 45G15
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 6958684
zbMATH Keywords: Caputo fractional differential equations
zbMATH Keywords: coupled integral boundary conditions
zbMATH Keywords: fixed point theorems
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1515/fca-2018-0024
OpenAlex ID: W2808615103
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DOI: 10.1515/FCA-2018-0024
published in: Fractional Calculus \ Applied Analysis
description: scientific article; zbMATH DE number 6958684