The heat equation is parabolic partial differential equation and occurs in the characterization of diffusion progress. In the present work, a new fractional operator based on the Rabotnov fractional‐exponential kernel is considered. Next, we conferred some fascinating and original properties of nominated new fractional derivative with some integral transform operators where all results are significant. The fundamental target of the proposed work is to solve the multidimensional heat equations of arbitrary order by using analytical approach homotopy perturbation transform method and residual power series method, where new fractional operator has been taken in new Yang‐Abdel‐Aty‐Cattani (YAC) sense. The obtained results indicate that solution converges to the original solution in language of generalized Mittag‐Leffler function. Three numerical examples are discussed to draw an effective attention to reveal the proficiency and adaptability of the recommended methods on new YAC operator.

中文翻译：

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使用新的Yang-Abdel-Aty-Cattani分式算子对扩散过程中的热方程进行分析

热方程是抛物线偏微分方程，出现在扩散过程的表征中。在当前的工作中，考虑了一个基于Rabotnov分数-指数核的新分数运算符。接下来，我们为提名的新分数导数提供了一些令人着迷的原始属性，以及一些积分变换算子，这些算子的所有结果都很重要。拟议工作的基本目标是通过使用解析方法同伦扰动变换方法和残差幂级数方法来求解任意阶的多维热方程，其中在新的Yang-Abdel-Aty-Cattani（YAC）中采用了新的分数算子感。获得的结果表明，在广义Mittag-Leffler函数语言中，解收敛于原始解。