In this article, two radial basis functions based collocation schemes, differentiated and integrated methods (DRBF and IRBF), are extended to solve a class of nonlinear fractional initial and boundary value problems. Before discretization, the nonlinear problem is linearized using generalized quasilinearization. An interesting proof via generalized monotone quasilinearization for the existence and uniqueness for fractional order initial value problem is given. This convergence analysis also proves quadratic convergence of the generalized quasilinearization method. Both the schemes are compared in terms of accuracy and convergence and it is found that IRBF scheme handles inherent RBF ill-condition better than corresponding DRBF method. Variety of numerical examples are provided and compared with other available results to confirm the efficiency of the schemes.

中文翻译：

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基于直接和积分径向函数的非线性分数阶微分方程拟线性化方案

在本文中，两个基于径向基函数的搭配方案，微分和积分方法（DRBF 和 IRBF）被扩展到解决一类非线性分数初值和边值问题。在离散化之前，非线性问题使用广义拟线性化进行线性化。给出了分数阶初值问题的存在唯一性通过广义单调拟线性化的有趣证明。这种收敛性分析也证明了广义拟线性化方法的二次收敛性。两种方案在精度和收敛性方面进行了比较，发现IRBF方案比相应的DRBF方法更好地处理固有的RBF病态。