This work adopts to the time-fractional Klein–Gordon equation (FKGE) in the Caputo sense. We present a new technique using the clique polynomial as basis function for the operational matrices to obtain solution of time-FKGE. The key advantage of this technique is converting the time-FKGE to algebraic equations, which can be simply solved the problem under study. For the approximation of a bivariate function using the clique polynomial, an error bound is given. Numerical results derived using the proposed technique are compared with the exact solution. The results show that the proposed technique is very user friendly for solving the time-FKGE and accurate.

这项工作采用了Caputo意义上的时间分数Klein-Gordon方程（FKGE）。我们提出了一种新技术，该技术使用集团多项式作为运算矩阵的基函数来获得时间FKGE的解。该技术的主要优点是将时间FKGE转换为代数方程，可以简单地解决正在研究的问题。对于使用集团多项式逼近二元函数的情况，给出了一个误差范围。将使用所提出的技术得出的数值结果与精确解进行比较。结果表明，所提出的技术对于解决时间FKGE问题具有很高的用户友好性和准确性。