A new extended cubic B-spline (ECBS) approximation is formulated, analyzed and applied to obtain the numerical solution of the time fractional Klein–Gordon equation. The temporal fractional derivative is estimated using Caputo’s discretization and the space derivative is discretized by ECBS basis functions. A combination of Caputo’s fractional derivative and the new approximation of ECBS together with [Formula: see text]-weighted scheme is utilized to obtain the solution. The method is shown to be unconditionally stable and convergent. Numerical examples indicate that the obtained results compare well with other numerical results available in the literature.

中文翻译：

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非线性时间分数克莱因-戈登方程的扩展三次B样条新逼近的发展与分析

制定、分析和应用了一种新的扩展三次 B 样条 (ECBS) 近似，以获得时间分数克莱因 - 戈登方程的数值解。时间分数导数使用 Caputo 离散化估计，空间导数使用 ECBS 基函数离散化。Caputo 的分数导数和 ECBS 的新近似与 [公式：见文本] 加权方案的组合用于获得解决方案。该方法被证明是无条件稳定和收敛的。数值例子表明，所获得的结果与文献中可用的其他数值结果相比很好。