MMN-2230

Existence of solutions for fractional interval-valued differential equations by the method of upper and lower solutions

  • Yong Huang, Baise University, Department of Mathematics, Baise 533000, Guangxi Province, P.R. China, yonghuang99@126.com
  • Yunru Bai, Institute of Computer Science, Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Lojasiewicza 6, Krakow 30-348, Poland, yunrubai@163.com
  • Yiliang Liu, Guangxi Key Laboratory of Universities Optimization Control and Engineering Calculation and College of Sciences, Guangxi University for Nationalities, Nanning 530006, Guangxi Province, P.R. China, yiliangliu100@126.com
  • Iván Szántó, Departamento de Matemática, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaíso, Chile, ivan.szanto@usm.cl

Abstract

In this work we firstly study some important properties of fractional calculus for interval-valued functions and introduce the concepts of upper and lower solutions for interval-valued Caputo fractional differential equations. Then, we prove an existence result for interval-valued Caputo fractional differential equations by use of the method of upper and lower solutions. Finally several examples will be presented to illustrate our abstract results.


Vol. 18 (2017), No. 2, pp. 811-836
DOI: 10.18514/MMN.2017.2230


Download: MMN-2230