A sine-cosine wavelet method for the approximation solutions of the fractional Bagley-Torvik equation


TURAN DİNCEL A.

SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI, vol.40, no.1, pp.150-154, 2022 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.14744/sigma.2021.00033
  • Journal Name: SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI
  • Journal Indexes: Emerging Sources Citation Index, Academic Search Premier, Directory of Open Access Journals
  • Page Numbers: pp.150-154
  • Keywords: Sine-cosine wavelet, Bagley-Torvik equation, Caputo derivative, Block pulse function, RICCATI DIFFERENTIAL-EQUATIONS, NUMERICAL-SOLUTION, ORDER

Abstract

Fractional Bagley-Torvik differential equations can be used to model a variety of natural phenomena in many branches of applied mathematics and engineering in general. The focus of this study is on solving the fractional Bagley-Torvik equations by using sine-cosine wavelet. To this end, the operational matrix of fractional integration is obtained for sine-cosine wavelets. By utilizing this matrix, fractional Bagley-Torvik differential equation is transformed to a system of linear algebraic equations with unknown coefficients, which in turn can readily be solved using numerical solution methods. Test examples are provided to demonstrate the validity and efficiency of this approach.