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On the Heat and Wave Equations with the Sturm-Liouville Operator in Quantum Calculus.
- Source :
-
Abstract & Applied Analysis . 1/19/2023, p1-8. 8p. - Publication Year :
- 2023
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10853375
- Database :
- Academic Search Index
- Journal :
- Abstract & Applied Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 161401678
- Full Text :
- https://doi.org/10.1155/2023/2488165