Scientific Research and Essays

  • Abbreviation: Sci. Res. Essays
  • Language: English
  • ISSN: 1992-2248
  • DOI: 10.5897/SRE
  • Start Year: 2006
  • Published Articles: 2748

Full Length Research Paper

Haar Wavelet-Picard technique for fractional order nonlinear initial and boundary value problems

Umer Saeed
  • Umer Saeed
  • School of Natural Sciences, National University of Sciences and Technology, Sector H-12, Islamabad, Pakistan.
  • Google Scholar
Mujeeb ur Rejman
  • Mujeeb ur Rejman
  • School of Natural Sciences, National University of Sciences and Technology, Sector H-12, Islamabad, Pakistan.
  • Google Scholar
Muhammad Asad Iqbal
  • Muhammad Asad Iqbal
  • Department of Mathematics, Faculty of Sciences, HITEC University Taxila, Pakistan.
  • Google Scholar


  •  Received: 18 December 2013
  •  Accepted: 28 February 2014
  •  Published: 30 June 2014

Abstract

In this article, a technique called Haar wavelet-Picard technique is proposed to get the numerical solutions of nonlinear differential equations of fractional order. Picard iteration is used to linearize the nonlinear fractional order differential equations and then Haar wavelet method is applied to linearized fractional ordinary differential equations. In each iteration of Picard iteration, solution is updated by the Haar wavelet method. The results are compared with the exact solution.

 

Key words: Fractional differential equations, Wavelet analysis, Caputo derivative, Haar wavelets, Picard iteration.