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Title

NUMERICAL ANALYSIS OF FRACTIONAL DIFFERENTIAL EQUATION BY WAVELETS

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Abstract

 IN THIS PAPER, WE INTRODUCE METHODS BAISED ON OPERATIONAL MATRIX OF FRACTIONAL INTEGRATION FOR SOLVING A TYPICAL N-TERM NON-HOMOGENEOUS FRACTIONAL DIFFERENTIAL EQUATION (FDE). WE USE BLOCK-PULS, HAAR WAVLETES AND HYBRID OF BLOCK-PULSE FUNCTIONS AND SHIFTED LEGENDRE POLYNOMIALS MATRICES OF FRACTIONAL INTEGRATION WHERE A FRACTIONAL DERIVATIVE IS DEFINED IN THE CAPUTO SENSE. BY USES THESE METHODS WE TRANSLATE AN FDE TO AN ALGEBRIC LIEAR EQUATIONS. METHODS HAS BEEN TESTED BY SOME NUMERICAL EXAMPLES.

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