Legendre wavelet operational matrix method for solving fractional differential equations in some special conditions
Thermal Science, vol.23, 2019 (SCI-Expanded, Scopus)
- 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: Caputo fractional derivative, Fractional differential equations, Legendre wavelets, Operational matrix
- Open Archive Collection: AVESIS Open Access Collection
- Istanbul Gelisim University Affiliated: Yes
Abstract
© 2019 Society of Thermal Engineers of Serbia.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.