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Quantum Extensions of Widder’s Formula via q‐Deformed Calculus

Author

Listed:
  • S. S. Naina Mohammed
  • K. Jeevanandham
  • A. Ramalingam
  • R. Maheswari
  • Prasantha Bharathi Dhandapani
  • Rebecca Muhumuza Nalule

Abstract

In this study, we rigorously established q‐Widder’s formula of first and second kind by employing the q‐integral within a quantum calculus framework. Our approach introduces a novel formulation of the inverse q‐Laplace transform, enabling simplified computation without relying on conventional complex integration methods. Several illustrative problems are solved to demonstrate the effectiveness of the proposed method. The results contribute to the theoretical foundation of q‐calculus and have potential applications in areas such as q‐quantum mechanics and the analysis of q‐special functions.

Suggested Citation

  • S. S. Naina Mohammed & K. Jeevanandham & A. Ramalingam & R. Maheswari & Prasantha Bharathi Dhandapani & Rebecca Muhumuza Nalule, 2025. "Quantum Extensions of Widder’s Formula via q‐Deformed Calculus," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jnljam:v:2025:y:2025:i:1:n:5525705
    DOI: 10.1155/jama/5525705
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    References listed on IDEAS

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    1. Thomas Ernst, 2012. "A Comprehensive Treatment of q-Calculus," Springer Books, Springer, edition 127, number 978-3-0348-0431-8, March.
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