Legendre wavelet method for solving fractional integro-differential equations of Bratu-type

This paper used Legendre wavelet to solve the numerical solution of fractional integro-differential equations of Bratu-type. Combing the definition of Legendre wavelet and its property, this study gave the Legendre wavelet operational matrix of fractional integration and transformed the initial problems into a system of algebraic equations using the obtained operational matrix. This system can be solved by using the computer which simplified the computation in great deal. Uniqueness theorem shows that the solution of this problem is unique. The results show that the more points, the higher the precision of the numerical solution. Numerical examples were included to demonstrate the validity and applicability of the technique.