In this paper, a numerical approach for solving the nonlinear space-time fractional partial differential equations with variable coefficients is proposed. The fractional derivatives are described in the conformable sense. The numerical approach is based on shifted Chebyshev polynomials of the second kind and finite difference method. The proposed scheme reduces the main problem to a system of nonlinear algebraic equations. The validity and the applicability of the proposed technique are shown by numerical examples.

中文翻译：

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非线性协调时空分数阶偏微分方程的数值解

本文提出了一种求解变系数非线性时空分数阶偏微分方程的数值方法。分数导数是在符合的意义上描述的。数值方法基于第二类移动切比雪夫多项式和有限差分方法。所提出的方案将主要问题简化为非线性代数方程组。数值例子表明了所提出技术的有效性和适用性。