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Novel integral transform treating some Ψ-fractional derivative equations

Chamekh Mourad, Latrache Mohamed Ali, Elzaki Tarig M.

Acta Mechanica et Automatica

2024

Vol. 18, no. 3

571--578

The paper deals with a new integral transformation method called Ψ-Elzaki transform (PETM) in order to analyze some Ψ-fractional differential equations. The proposed method uses a modification of the Elzaki transform that is well adapted to deal with Ψ-fractional operators. To solve the nonlinear Ψ-fractional differential equations, we combine the PETM by an iterative method to overcome this nonlinearity. To validate the accuracy and efficiency of this approach, we compare the results of the discussed numerical examples with the exact solutions.