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

Serikbol Shaimardan, Lars-Erik Persson, Nariman Tokmagambetov and Douglas R. Anderson

Abstract and Applied Analysis, 2022, vol. 2022, 1-8

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: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:2488165

DOI: 10.1155/2022/2488165

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