AUTHOR=Tao Huiqiang , Anjum Naveed , Yang Yong-Ju TITLE=The Aboodh transformation-based homotopy perturbation method: new hope for fractional calculus JOURNAL=Frontiers in Physics VOLUME=11 YEAR=2023 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2023.1168795 DOI=10.3389/fphy.2023.1168795 ISSN=2296-424X ABSTRACT=

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.