Solving fractional nonlinear Fredholm integro-differential equations by the second kind Chebyshev wavelet

In this paper, we first construct the second kind Chebyshev wavelet. Then we present a computational method based on the second kind Chebyshev wavelet for solving a class of nonlinear Fredholm integro-differential equations of fractional order. The second kind Chebyshev wavelet operational matrix of fractional integration is derived and used to transform the equation to a system of algebraic equations. The method is illustrated by applications and the results obtained are compared with the existing ones in open literature. Moreover, comparing the methodology with the known technique shows that the present approach is more efficient and more accurate.

► We solve fractional nonlinear Fredholm integro-differential equation by wavelet.
► Construct the second kind Chebyshev wavelet.
► Derive operational matrix of fractional integration of the second kind Chebyshev wavelet.
► The proposed method improve the accuracy of numerical solutions.