Solving Nonlinear Fractional Partial Differential Equations Using the Elzaki Transform Method and the Homotopy Perturbation Method

• Published in: Abstract and applied analysis Vol. 2022; pp. 1 - 9
• Main Authors: Mohamed, Mohamed. Z., Yousif, Mohammed, Hamza, Amjad E.
• Format: Journal Article
• Language: English
• Published: New York Hindawi 2022; John Wiley & Sons, Inc; Wiley
• Subjects: Applied mathematics; Approximation; Boundary value problems; Differential equations, Partial; Fractional calculus; Initial conditions; Integral equations; Mathematical research; Nonlinear differential equations; Partial differential equations; Perturbation (Mathematics); Perturbation methods; Transformations (Mathematics); Saudi Arabia
• ISSN: 1085-3375; 1687-0409
• DOI: 10.1155/2022/4743234

In this paper, we combine the Elzaki transform method (ETM) with the new homotopy perturbation method (NHPM) for the first time. This hybrid approach can solve initial value problems numerically and analytically, such as nonlinear fractional differential equations of various normal orders. The Elzaki transform method (ETM) is used to solve nonlinear fractional differential equations, and then the homotopy is applied to the transformed equation, which includes the beginning conditions. To obtain the solution to an equation, we use the inverse transforms of the Elzaki transform method (ETM). The initial conditions have a big impact on the equation’s result. We give three beginning value issues that were solved as precise or approximation solutions with high rigor to demonstrate the method’s power and correctness. It is clear that solving nonlinear partial differential equations with the crossbred approach is the best alternative.