Convergence analysis of the Legendre wavelets method for a class of Fredholm-Volterra integro-differential equations of fractional-order

In this paper, we develop a Legendre wavelets method for the numerical solution of Fredholm-Volterra integro-differential equations of fractional order. The Caputo sense is used to explain the fractional derivative operator. The proposed scheme is verified by presenting examples that their exact solutions are available. Numerical results show that the approximation errors decay exponentially in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>-norm.