A Fractional spectral method for weakly singular Volterra integro-differential equations with delays of the third-kind
<|reference_start|>A Fractional spectral method for weakly singular Volterra integro-differential equations with delays of the third-kind: In this paper, we present a fractional spectral collocation method for solving a class of weakly singular Volterra integro-differential equations (VDIEs) with proportional delays and cordial operators. Assuming the underlying solutions are in a specific function space, we derive error estimates in the $L^2_{\omega^{\alpha,\beta,\lambda}}$ and $L^{\infty}$-norms. A rigorous proof reveals that the numerical errors decay exponentially with the appropriate selections of parameters $\lambda$. Subsequently, numerical experiments are conducted to validate the effectiveness of the method.<|reference_end|>
@article{zhao2024a,
    title={A Fractional spectral method for weakly singular Volterra
  integro-differential equations with delays of the third-kind},
    author={Borui Zhao},
    journal={arXiv preprint arXiv:2409.10861},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.10861},
    primaryClass={math.NA cs.NA}
}