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September 10, 2025Afyon Kocatepe University Journal of Sciences and EngineeringOpen Access

Theory and Applications of the Double Laplace Transform for Local Deri̇vati̇ves Wi̇th the Mittag Leffler Kernel

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Authors

BÖBurak ÖzküçükEBErdal Baş

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Overview

This article defines the M-derivative double Laplace transform and applies it to fractional differential equations, suggesting new methods for solutions.

Key Points

  • The M-derivative double Laplace transform defines a new approach for fractional differential equations.
  • This method incorporates the Mittag-Leffler function, facilitating solutions to complex equations.
  • Theorems presented in this work enhance the applicability of this method in diverse mathematical fields.
  • Finding solutions to partial differential equations using M-derivatives can benefit engineering and physical models.

Cite This Study

Özküçük et al. (2025) studied this question.

synapsesocial.com/papers/68c1ad5554b1d3bfb60e51f8https://doi.org/10.35414/akufemubid.1569312
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Theory and Applications of the Triple Laplace Transform for Local Derivative with the Mittag Leffler Kernel2026
  2. 2Modified double Laplace transform of partial derivatives and its applications2024
  3. 3A New Laplace-Type Transform on Weighted Spaces with Applications to Hybrid Fractional Cauchy Problems2025
  4. 4Generalized Deformable Fractional Derivative via the Mittag-Leffler Function: Fundamental Properties, Integral Representation, and Applications2025
  5. 5Theory on Linear L-Fractional Differential Equations and a New Mittag–Leffler-Type Function2024 · 8 citations