Computational methods for fractional differential equations exhibit essential instability. Even a minor modification of the coefficients or other entry data may switch good results to the divergent. The goal of this paper is to suggest the reliable dual approach which fixes this inconsistency. We suggest to use two parallel methods based on the transformation of fractional derivatives through integration by parts or by means of substitution. We introduce the method of substitution and choose the proper discretization scheme that fits the grid points for the by-parts method. The solution is reliable only if both methods produce the same results. As an additional control tool, the Taylor series expansion allows to estimate the approximation errors for fractional derivatives. In order to demonstrate the proposed dual approach, we apply it to linear, quasilinear and semilinear equations and obtain very good precision of the results. The provided examples and counterexamples support the necessity to use the dual approach because either method, used separately, may produce incorrect results. The order of the exactness is close to the exactness of fractional derivatives approximations.

翻译：分差方程的计算方法显示出基本的不稳定性。即使对系数或其他输入数据稍作修改,也可能把好的结果转换为不同的结果。本文件的目的是提出纠正这种不一致的可靠的双向方法。我们建议采用两种平行方法,根据分数衍生物通过部件或替代手段的整合转化来改变分数衍生物。我们引入替代方法,并选择适合按部分计算法的网格点的适当分化办法。只有在两种方法产生相同结果的情况下,解决办法才可靠。作为一种额外的控制工具,泰勒系列的扩展可以估计分数衍生物的近似误差。为了证明拟议的双向法,我们将其应用于线性、准线性和半线性方程性方程性方程,并获得非常精确的结果。所提供的示例和反实例支持使用双向法的必要性,因为这两种方法分别使用,都可能产生不正确的结果。精确性顺序接近分数衍生物近的准确性。