THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

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Aydin Secer

,

Selvi Altun

,

Mustafa Bayram

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

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 FDEs into a system of algebraic equations. Finally, the introduced tecnique is tested on several illustrative examples. The obtained results demonstrate that this technique is a very impressive and applicable mathematical tool for solving FDEs.
KEYWORDS
operational matrix, legendre wavelets, caputo fractional derivative, fractional differential equations
PAPER SUBMITTED: 2018-09-20
PAPER REVISED: 2018-10-24
PAPER ACCEPTED: 2019-01-10
PUBLISHED ONLINE: 2019-03-09
DOI REFERENCE: https://doi.org/10.2298/TSCI180920034S
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Supplement 1, PAGES [S203 - S214]
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Legendre wavelet operational matrix method for solving fractional differential equations in some special conditions

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