On the Heat and Wave Equations with the Sturm-Liouville Operator in Quantum Calculus
Shaimardan S. Persson L.-E. Tokmagambetov N.
2023Hindawi Limited
Abstract and Applied Analysis
2023#2023
In this paper, we explore a generalised solution of the Cauchy problems for the q-heat and q-wave equations which are generated by Jacksons 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.
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L. N. Gumilyov Eurasian National University, Astana, Kazakhstan
Department of Mathematics and Computer Science, Karlstad University, Karlstad, Sweden
Department of Computer Science and Computational Engineering, Campus Narvik, The Arctic University of Norway, Narvik, Norway
Karagandy University of the Name of Academician E.A. Buketov, Karaganda, Kazakhstan
L. N. Gumilyov Eurasian National University
Department of Mathematics and Computer Science
Department of Computer Science and Computational Engineering
Karagandy University of the Name of Academician E.A. Buketov
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026