LEGENDRE WAVELET OPERATIONAL MATRIX METHOD FOR SOLVING FRACTIONAL DIFFERENTIAL EQUATIONS IN SOME SPECIAL CONDITIONS

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Seçer A., Altun S., Bayram M.

THERMAL SCIENCE, vol.23, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 23
  • Publication Date: 2019
  • Doi Number: 10.2298/tsci180920034s
  • Journal Name: THERMAL SCIENCE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: operational matrix, Legendre wavelets, Caputo fractional derivative, fractional differential equations
  • Yıldız Technical University Affiliated: Yes

Abstract

This paper proposes a new technique which rests upon Legendre wavelets for solving linear and non-linear forms of fractional order initial and boundary value problems. In some particular circumstances, a new operational matrix of fractional derivative is generated by utilizing some significant properties of wavelets and orthogonal polynomials. We approached the solution in a finite series with respect to Legendre wavelets and then by using these operational matrices, we reduced the fractional differential equations into a system of algebraic equations. Finally, the introduced technique is tested on several illustrative examples. The obtained results demonstrate that this technique is a very impressive and applicable mathematical tool for solving fractional differential equations.