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

Abstract

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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.

Keywords

• homotopy perturbation method
• Aboodh transform
• He’s polynomials
• fractional differential equation
• two-scale fractal theory