Operator (biology)

Heat kernel

Pure mathematics

Mathematics

Differential operator

Gene

Fractional calculus

Semi-elliptic operator

Repressor

Heat equation

Transcription factor

Biochemistry

Integral transform

Partial differential equation

Applied mathematics

Mathematical analysis

Chemistry

Kernel (algebra)

Mathematical Methods in the Applied Sciences

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.

An analysis for heat equations arises in diffusion process using new Yang‐Abdel‐Aty‐Cattani fractional operator