Extremal solutions for nonlinear fractional boundary value problems with P-Laplacian

Youzheng Ding ^[1] ; Zhongli Wei ^[1] ; Jiafa Xu ^[2] ; Donal O'Regan ^[3]
1. [1] Shandong Jianzhu University
  
  Shandong Jianzhu University
  
  China
2. [2] Chongqing Normal University
  
  Chongqing Normal University
  
  China
3. [3] National University of Ireland
  
  National University of Ireland
  
  Irlanda
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Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 288, Nº 1 (November 2015), 2015, págs. 151-158
Idioma: inglés
DOI: 10.1016/j.cam.2015.04.002
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Resumen
- In this paper we investigate the existence and uniqueness of extremal solutions for nonlinear boundary value problems of a fractional p-Laplacian differential equation involving Riemann–Liouville derivatives. We construct two well-defined monotone iterative sequences of upper and lower solutions which converge uniformly to the actual solution of the problem. A numerical iterative scheme is also introduced to obtain an accurate approximate solution for the problem and an example is presented to illustrate the results.