We provide a new effective method for the two-dimensional distributed-order fractional differential equations (DOFDEs). The technique is based on fractional-order Chebyshev wavelets. An exact formula involving regularized beta functions for determining the Riemann-Liouville fractional integral operator of these wavelets is given. The given wavelets and this formula are utilized to find the solutions of the given two-dimensional DOFDEs. The method gives very accurate results. The given numerical examples support this claim.

中文翻译：

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二维分布式分数阶微分方程的广义分数阶Chebyshev小波方法

我们为二维分布式分数阶微分方程（DOFDE）提供了一种新的有效方法。该技术基于分数阶切比雪夫小波。给出了用于确定这些小波的Riemann-Liouville分数积分算子的包含正则β函数的精确公式。利用给定的小波和该公式可以找到给定的二维自由度的解。该方法给出了非常准确的结果。给出的数字示例支持该主张。