• DOI:10.1007/s13540-022-00113-4
• Corpus ID: 250492944

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

@article{Faghih2022ASA,
  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},
  year={2022},
  volume={26},
  pages={370-398}
}

• A. Faghih, M. 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 solving complex non-linear algebraic system. Furthermore, the well-known exponential accuracy is established in $$L^{2}$$ L 2 -norm, and we provide some examples to illustrate the theoretical results and the performance of the proposed method.