This paper aims to investigate numerical solution of time fractional modified Burgers’ equation via Caputo fractional derivative. Extended cubic B-spline collocation scheme which reduces the nonlinear equation to a system of linear equation in the matrix form has been used for this investigation. The nonlinear part in fractional partial differential equation has been linearized by modified form of the existing method. The validity of proposed scheme has been examined on three test problems and effect of viscosity \(\nu \) and \(\alpha \ \epsilon \ [0, 1]\) variation displayed in 2D and 3D graphics. Moreover, the working of proposed scheme has also been explained through algorithm and stability of proposed scheme has been analyzed by von Neumann scheme and has proved to be unconditionally stable. To quantify the accuracy of suggested scheme, error norms have been computed.

中文翻译：

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扩展三次B样条方法对时间分数修正Burgers方程解的近似

本文旨在通过Caputo分数阶导数研究时间分数修正Burgers方程的数值解。这项研究使用了扩展的三次B样条搭配方案，该方案将非线性方程简化为矩阵形式的线性方程组。分数阶偏微分方程中的非线性部分已通过现有方法的改进形式线性化。已针对三个测试问题以及粘度\（\ nu \）和\（\ alpha \ \ epsilon \ [0，1] \）的影响检验了所提方案的有效性。以2D和3D图形显示的变化。此外，还通过算法解释了该方案的工作，并通过冯·诺依曼方案分析了该方案的稳定性，并证明了该方案是无条件稳定的。为了量化建议方案的准确性，已经计算了误差范数。