Abstract In this work, we deal with the quasilinearization technique for a class of nonlinear Riemann-Liouville fractional-order two-point boundary value problems. Using quasilinearization technique, we construct a monotone sequence of approximate solutions which has quadratic convergence to the unique solution of the original problem, and establish the corresponding convergence estimates. Moreover, the performance of the technique is examined through a numerical example, which shows that our regularization method is available and stable.

中文翻译：

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求解非线性 Riemann-Liouville 分数阶问题的拟线性化技术

摘要 在这项工作中，我们处理一类非线性 Riemann-Liouville 分数阶两点边值问题的拟线性化技术。利用拟线性化技术，构造一个对原问题的唯一解具有二次收敛性的近似解的单调序列，并建立相应的收敛估计。此外，通过一个数值例子来检验该技术的性能，这表明我们的正则化方法是可用且稳定的。