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

S. S. Naina Mohammed, K. Jeevanandham, A. Ramalingam, R. Maheswari, Prasantha Bharathi Dhandapani and Rebecca Muhumuza Nalule

Journal of Applied Mathematics, 2025, vol. 2025, 1-10

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.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:5525705

DOI: 10.1155/jama/5525705

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