The construction of operational matrices of integral and fractional integral using the flatlet oblique multiwavelets

Abdi-Mazraeh S., Lakestanı M., Dehghan M.

JVC/Journal of Vibration and Control, vol.21, no.4, pp.818-832, 2015 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 4
  • Publication Date: 2015
  • Doi Number: 10.1177/1077546313490430
  • Journal Name: JVC/Journal of Vibration and Control
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.818-832
  • Keywords: Abel integral equation, biorthogonal system, flatlet oblique multiwavelets, operational matrix, Riemann-Liouville integral operator
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

The main aim of this paper is to introduce the operational matrices of integral and fractional integral using the flatlet oblique multiwavelets. The operational matrices of integral and fractional integrals for flatlet scaling functions and wavelets are presented and are utilized to reduce the solution of the Abel integral equations of the first and the second kinds to the solution of algebraic equations. The main characteristic behind our approach in using this technique is that only a small number of flatlet oblique multiwavelets is needed to obtain a satisfactory result. Illustrative examples reveal that the present method is very effective and convenient.