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Fractional Calculus and Applied Analysis

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Monotone iterative method for a class of nonlinear fractional differential equations

Guotao Wang
  • School of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi, 041004, People’s Republic of China
  • Email:
/ Dumitru Baleanu
  • Department of Mathematics Faculty of Art and Sciences, Cankaya University, Balgat, Ankara, 06530, Turkey
  • Institute of Space Sciences, Magurele - Bucharest, Romania
  • Email:
/ Lihong Zhang
  • School of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi, 041004, People’s Republic of China
  • Email:
Published Online: 2012-03-18 | DOI: https://doi.org/10.2478/s13540-012-0018-z

Abstract

By applying the monotone iterative technique and the method of lower and upper solutions, this paper investigates the existence of extremal solutions for a class of nonlinear fractional differential equations, which involve the Riemann-Liouville fractional derivative D q x(t). A new comparison theorem is also build. At last, an example is given to illustrate our main results.

MSC: Primary 26A33; Secondary 34A08

Keywords: monotone iterative technique; nonlinear fractional differential equation; comparison theorem; extremal solutions

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About the article

Published Online: 2012-03-18

Published in Print: 2012-06-01


Citation Information: Fractional Calculus and Applied Analysis, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.2478/s13540-012-0018-z.

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© 2012 Diogenes Co., Sofia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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