Uniqueness and stability of coupled sequential fractional differential equations with boundary conditions
type: Item
instance of: scholarly article
title: Uniqueness and stability of coupled sequential fractional differential equations with boundary conditions
author: Areen Al-Khateeb
author: Naser A. Al-O'dat
author: Ayman A. Hazaymeh
author: Ra'ed Hatamleh
published in: Rocky Mountain Journal of Mathematics
publication date: 2022-10-10T00:00:00Z
full work available at URL: rmj.2022.52.1227.full
review text: In this paper, the authors study the following coupled system of nonlinear Caputo sequential fractional differential equations of the form \[ \begin{cases} ^{C}D^{(\alpha+1)}(D+k)u(t)=f(t,u(t),v(t)), \quad t\in [0,T], 1<a\leq 2, k>0,\\ {}^{C}D^{(\beta-1)}(D+k)u(t)=g(t,u(t),v(t)), \quad t\in [0,T], 1<\beta\leq 2, k>0,\\ u(0)=\lambda v'(T), \quad u'(0)=0,\\ v(0)=\mu u'(T), \quad v'(0)=0, \end{cases} \] where \({}^{C}D^{\xi}\) denote the Caputo fractional derivatives of order \(\xi\in\{\alpha,\beta\}\), \(f,g: [0,T]\times \mathbb{R}\to \mathbb{R}\) are given continuous functions and \(\lambda, \mu\) are real constants. Existence and uniqueness results are obtained via Banach fixed point theorem and Leray-Schauder alternative. Also Ulam-Hyers stability for the given problem is studied. The main results are well-illustrated with the aid of a numerical example.
reviewed by: Sotiris K. Ntouyas
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34D10
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 34B08
zbMATH DE Number: 7598556
zbMATH Keywords: ractional derivative
zbMATH Keywords: fixed-point theorem
zbMATH Keywords: fractional differential equation
Wikidata QID: Q115240003
MaRDI profile type: Publication
OpenAlex ID: W4312609887
cites work: Boundary value problems for a class of sequential integrodifferential equations of fractional order
cites work: Q4421936
cites work: Q5699297
cites work: Q3141902
cites work: Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
cites work: Advances in Fractional Calculus
DOI: 10.1216/RMJ.2022.52.1227
description: scientific article; zbMATH DE number 7598556