Solution set for fractional differential equations with Riemann-Liouville derivative

Yurilev Chalco-Cano; Juan J. Nieto; Abdelghani Ouahab; Heriberto Román-Flores

doi:10.2478/s13540-013-0043-6

Solution set for fractional differential equations with Riemann-Liouville derivative

Yurilev Chalco-Cano
, Juan J. Nieto
, Abdelghani Ouahab
, Heriberto Román-Flores

Department of Mathematics

University of Santiago de Compostela
King Abdulaziz University
University of Sidi-Bel-Abbès
Universidad de Tarapacá

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

We study an initial value problem for a fractional differential equation using the Riemann-Liouville fractional derivative. We obtain some topological properties of the solution set: It is the intersection of a decreasing sequence of compact nonempty contractible spaces. We extend the classical Kneser's theorem on the structure solution set for ordinary differential equations.

Original language	English
Pages (from-to)	682-694
Number of pages	13
Journal	Fractional Calculus and Applied Analysis
Volume	16
Issue number	3
DOIs	https://doi.org/10.2478/s13540-013-0043-6
State	Published - Sep 2013

Keywords

Kneser's theorem
acyclic set
fractional derivative
fractional differential equations
fractional integral

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10.2478/s13540-013-0043-6

Cite this

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title = "Solution set for fractional differential equations with Riemann-Liouville derivative",

abstract = "We study an initial value problem for a fractional differential equation using the Riemann-Liouville fractional derivative. We obtain some topological properties of the solution set: It is the intersection of a decreasing sequence of compact nonempty contractible spaces. We extend the classical Kneser's theorem on the structure solution set for ordinary differential equations.",

keywords = "Kneser's theorem, acyclic set, fractional derivative, fractional differential equations, fractional integral",

author = "Yurilev Chalco-Cano and Nieto, \{Juan J.\} and Abdelghani Ouahab and Heriberto Rom{\'a}n-Flores",

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AU - Chalco-Cano, Yurilev

AU - Nieto, Juan J.

AU - Ouahab, Abdelghani

AU - Román-Flores, Heriberto

PY - 2013/9

Y1 - 2013/9

N2 - We study an initial value problem for a fractional differential equation using the Riemann-Liouville fractional derivative. We obtain some topological properties of the solution set: It is the intersection of a decreasing sequence of compact nonempty contractible spaces. We extend the classical Kneser's theorem on the structure solution set for ordinary differential equations.

AB - We study an initial value problem for a fractional differential equation using the Riemann-Liouville fractional derivative. We obtain some topological properties of the solution set: It is the intersection of a decreasing sequence of compact nonempty contractible spaces. We extend the classical Kneser's theorem on the structure solution set for ordinary differential equations.

KW - Kneser's theorem

KW - acyclic set

KW - fractional derivative

KW - fractional differential equations

KW - fractional integral

UR - https://www.scopus.com/pages/publications/84879778444

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DO - 10.2478/s13540-013-0043-6

M3 - Article

AN - SCOPUS:84879778444

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VL - 16

SP - 682

EP - 694

JO - Fractional Calculus and Applied Analysis

JF - Fractional Calculus and Applied Analysis

IS - 3

ER -

Solution set for fractional differential equations with Riemann-Liouville derivative

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Keywords

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