A Haar wavelet operational matrix is applied to fractional integration, which has not been undertaken before. The Haar wavelet approximating method is used to reduce the fractional Volterra and Abel integral equations to a system of algebraic equations. A global error bound is estimated and some numerical examples with smooth, nonsmooth, and singular solutions are considered to demonstrate the validity and applicability of the developed method.
In this paper, two methods based on CAS wavelets and Legendre polynomials are applied to approximate the solutions of a kind of fractional Volterra integral equations called weakly singular integral equations. The methods are compared presenting some examples.
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