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On the double Laplace transform with respect to another function

Author

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  • Lemnaouar, M.R.
  • Hakki, I. El

Abstract

This paper explores the generalized double Laplace transform (GDLT) and its applications in fractional calculus. We begin by establishing essential lemmas and definitions that form the foundation of our findings. The core properties of the GDLT are thoroughly examined, providing a comprehensive understanding of its characteristics. We present novel results related to fractional and classical partial derivatives, as well as the double convolution theorem. Additionally, we calculate the double generalized Laplace transform for various bivariate Mittag-Leffler functions. The practical utility of this new double integral transform is demonstrated through its application in solving a range of fractional partial differential equations, highlighting its significance in applied mathematics.

Suggested Citation

  • Lemnaouar, M.R. & Hakki, I. El, 2025. "On the double Laplace transform with respect to another function," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:chsofr:v:194:y:2025:i:c:s0960077925002504
    DOI: 10.1016/j.chaos.2025.116237
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    References listed on IDEAS

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    1. Ranjit R. Dhunde & G. L. Waghmare, 2016. "Double Laplace Transform Method for Solving Space and Time Fractional Telegraph Equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2016, pages 1-7, October.
    2. Vieira, N. & Ferreira, M. & Rodrigues, M.M., 2022. "Time-fractional telegraph equation with ψ-Hilfer derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    3. Kürt, Cemaliye & Fernandez, Arran & Özarslan, Mehmet Ali, 2023. "Two unified families of bivariate Mittag-Leffler functions," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    4. Li, Jing & Ma, Li, 2023. "A unified Maxwell model with time-varying viscosity via ψ-Caputo fractional derivative coined," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
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