On the Heat and Wave Equations with the Sturm‐Liouville Operator in Quantum Calculus

Serikbol Shaimardan, Lars-Erik Persson and Nariman Tokmagambetov

Abstract and Applied Analysis, 2023, vol. 2023, issue 1

Abstract: In this paper, we explore a generalised solution of the Cauchy problems for the q‐heat and q‐wave equations which are generated by Jackson’s and the q‐Sturm‐Liouville operators with respect to t and x, respectively. For this, we use a new method, where a crucial tool is used to represent functions in the Fourier series expansions in a Hilbert space on quantum calculus. We show that these solutions can be represented by explicit formulas generated by the q‐Mittag‐Leffler function. Moreover, we prove the unique existence and stability of the weak solutions.

Date: 2023
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https://doi.org/10.1155/2023/2488165

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2023:y:2023:i:1:n:2488165

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