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Abstract This paper deals with the numerical solution of a class of nonlinear multi-term weakly singular fractional Volterra integro-differential equations by Jacobi collocation method based on the orthogonal polynomials. Since the solution of the proposed equation is not smooth enought in the origin, thus the idea of the smoothing transformation is used on the equation to incearse the smoothness of the solution. We represent an operator-based discussion of smoothing transformation and Gauss-Jacobi quadrature for Riemann-Liouville integral operators and weakly singular integral operators using their similar constructions and extend it to the error analysis of the proposed method and obtain an error bound for the discrete collocation solution. To test the efficiency and accuracy, various numerical examples are solved by the proposed method and the obtained error results are in accordance with the convergence analysis of the method. 2020 MSC: 26A33, 65R20, 65M70
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Haddam et al. (2024) studied this question.
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