A spectral approach to non-linear weakly singular fractional integro-differential equations

  title={A spectral approach to non-linear weakly singular fractional integro-differential equations},
  author={Amin Faghih and Magda Rebelo},
  journal={Fractional Calculus and Applied Analysis},
  • A. FaghihM. Rebelo
  • Published 13 July 2022
  • Mathematics, Computer Science
  • Fractional Calculus and Applied Analysis
In this work, a class of non-linear weakly singular fractional integro-differential equations is considered, and we first prove existence, uniqueness, and smoothness properties of the solution under certain assumptions on the given data. We propose a numerical method based on spectral Petrov-Galerkin method that handling to the non-smooth behavior of the solution. The most outstanding feature of our approach is to evaluate the approximate solution by means of recurrence relations despite… 



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