In this paper, a sixth-kind Chebyshev collocation method will be considered for solving a class of variable order fractional nonlinear quadratic integro-differential equations (V-OFNQIDEs). The operational matrix of variable order fractional derivative for sixth-kind Chebyshev polynomials is derived and then, a collocation approach is employed to reduce the V-OFNQIDE to a system of nonlinear algebraic equations. Convergence analysis of the proposed method is evaluated and the rate of convergence is established. Finally, some numerical test examples are investigated to validate the accuracy and robustness of the proposed approach.

中文翻译：

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基于第六类契比雪夫搭配方法的分数阶非线性二次积分微分方程数值解

在本文中，将考虑使用第六种Chebyshev搭配方法来求解一类变量阶分数阶非线性二次积分微分方程（V-OFNQIDEs）。推导了六种Chebyshev多项式的变阶分数阶导数的运算矩阵，然后采用搭配方法将V-OFNQIDE简化为非线性代数方程组。对所提出方法的收敛性进行了评估，并确定了收敛速度。最后，研究了一些数值测试示例，以验证所提出方法的准确性和鲁棒性。