In this paper, a new reproducing kernel Chebyshev wavelets method of solving a fractional telegraph equation is proposed. For solving the equation, reproducing kernel Chebyshev wavelets bases is constructed based on Chebyshev polynomials with a parameter. We choose an improved differential quadrature method with fourth-order truncation error to approximate second-order derivative term of the equation. Subsequently, the fractional telegraph equation is transformed into integral equation and the best approximate solution is obtained by searching the minimum of \(\varepsilon \)-approximate solutions. It is satisfied that the accuracy of errors provided by examples is very high.

本文提出了一种求解分数电报方程的新的再现核Chebyshev小波方法。为了求解该方程，基于带参数的切比雪夫多项式构造再现核切比雪夫小波基。我们选择一种具有四阶截断误差的改进的微分正交方法来近似方程的二阶导数项。随后，将分数电报方程转换为积分方程，并通过搜索\（\ varepsilon \）近似解的最小值来获得最佳近似解。可以肯定的是，示例提供的错误的准确性非常高。