An analysis for heat equations arises in diffusion process using new Yang‐Abdel‐Aty‐Cattani fractional operator
By Sunil Kumar, Surath Ghosh, Bessem Samet, E. F. D. Goufo. Mathematical methods in the applied sciences, 2020
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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.
Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/99f407afb56203dd752c7eabd03f71834eef2d61
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Citations in the corpus
- On novel nondifferentiable exact solutions to local fractional Gardner's equation using an effective technique (2020, background): “(17) Now, let us apply the new variables (13) on Equation (12).”