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

dc.contributor.author	Shaimardan, Serikbol
dc.contributor.author	Persson, Lars-Erik
dc.contributor.author	Tokmagambetov, Nariman
dc.date.accessioned	2024-12-13T11:50:57Z
dc.date.available	2024-12-13T11:50:57Z
dc.date.issued	2023
dc.identifier.issn	1687-0409
dc.identifier.other	doi.org/10.1155/2023/2488165
dc.identifier.uri	http://rep.enu.kz/handle/enu/20223
dc.description.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.	ru
dc.language.iso	en	ru
dc.publisher	Hindawi Abstract and Applied Analysis	ru
dc.relation.ispartofseries	Volume 2023, Article ID 2488165, 8 pages;
dc.title	On the Heat and Wave Equations with the Sturm-Liouville Operator in Quantum Calculus	ru
dc.type	Article	ru