LEGENDRE WAVELET OPERATIONAL MATRIX METHOD FOR SOLVING FRACTIONAL DIFFERENTIAL EQUATIONS IN SOME SPECIAL CONDITIONS - Secer, Aydin; Altun, Selvi; Bayram, Mustafa (VINCA INST NUCLEAR SCI, 2019)
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.
Keywords: operational matrix; Legendre wavelets; Caputo fractional derivative; fractional differential equations; Thermodynamics