On the Heat and Wave Equations with the Sturm-Liouville Operator in Quantum Calculus
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 i...
Main Authors: | , , |
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Format: | Article |
Language: | English |
Published: |
Hindawi Limited
2023-01-01
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Series: | Abstract and Applied Analysis |
Online Access: | http://dx.doi.org/10.1155/2023/2488165 |
Summary: | 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. |
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ISSN: | 1687-0409 |