## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### 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**

PAPER SUBMITTED: 2018-09-20

PAPER REVISED: 2018-10-24

PAPER ACCEPTED: 2019-01-10

PUBLISHED ONLINE: 2019-03-09

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