The Aboodh transformation-based homotopy perturbation method: new hope for fractional calculus

Fractional differential equations can model various complex problems in physics and engineering, but there is no universal method to solve fractional models precisely. This paper offers a new hope for this purpose by coupling the homotopy perturbation method with Aboodh transform. The new hybrid tec...

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Bibliographic Details
Published in:Frontiers in physics 2023-04, Vol.11
Main Authors: Tao, Huiqiang, Anjum, Naveed, Yang, Yong-Ju
Format: Article
Language:English
Subjects:
Aboodh transform
fractional differential equation
He’s polynomials
homotopy perturbation method
two-scale fractal theory
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Summary:Fractional differential equations can model various complex problems in physics and engineering, but there is no universal method to solve fractional models precisely. This paper offers a new hope for this purpose by coupling the homotopy perturbation method with Aboodh transform. The new hybrid technique leads to a simple approach to finding an approximate solution, which converges fast to the exact one with less computing effort. An example of the fractional casting-mold system is given to elucidate the hope for fractional calculus, and this paper serves as a model for other fractional differential equations.
ISSN:2296-424X
2296-424X
DOI:10.3389/fphy.2023.1168795