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This article defines the M-derivative double Laplace transform and applies it to fractional differential equations, suggesting new methods for solutions.
This article aims to define the 𝑀-derivative double Laplace transform, which is the general form of the six-parameter conformable derivative involving the Mittag-Leffler function. It is expressed with several theorems and will give us a useful and dependable method for solving fractional 𝑀-derivative partial differenial equations. Furthermore, the application of these given definitions and theorems to fractional partial differential equations is shown. Finding solutions to partial differential equations containing 𝑀-derivatives that can match mathematical, engineering, and physical mode ls may be accomplished with the use of this transformation.
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Özküçük et al. (2025) studied this question.
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