On the double Laplace-typed integral transform for solving partial differential equations via quantum calculus
Authors
S. Jirakulchaiwong
- Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand.
K. Nonlaopon
- Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand.
Abstract
In this work, we extend double Laplace-type integral transform (DLTT) and apply the concept of quantum calculus or \(q\)-calculus to establish the definitions of double \(q\)-Laplace-type integral transform (\(q\)-DLTT). We present some main properties and compute some functions of the \(q\)-DLTT. Also, we apply them to establish simple formulas for the general solution to solve the \(q\)-PDEs, such as \(q\)-wave equation, \(q\)-Klein-Gordon equation, \(q\)-Laplace equation, \(q\)-heat equation, and \(q\)-telegraph equation. By using the Mathematica program, the 3D plots, which represent for the \(q\)-PDEs, are provided. Finally, a convergence comparison between the exact solution and \(q\)-calculus of PDEs is also given in this research.
Share and Cite
ISRP Style
S. Jirakulchaiwong, K. Nonlaopon, On the double Laplace-typed integral transform for solving partial differential equations via quantum calculus, Journal of Mathematics and Computer Science, 38 (2025), no. 2, 236--251
AMA Style
Jirakulchaiwong S., Nonlaopon K., On the double Laplace-typed integral transform for solving partial differential equations via quantum calculus. J Math Comput SCI-JM. (2025); 38(2):236--251
Chicago/Turabian Style
Jirakulchaiwong, S., Nonlaopon, K.. "On the double Laplace-typed integral transform for solving partial differential equations via quantum calculus." Journal of Mathematics and Computer Science, 38, no. 2 (2025): 236--251
Keywords
- \(q\)-Laplace-typed integral transform
- \(q\)-derivative
- \(q\)-integral
- \(q\)-calculus
- \(q\)-patial differential equations
- \(q\)-convolution theorem
MSC
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