On the double Laplace-typed integral transform for solving partial differential equations via quantum calculus

Volume 38, Issue 2, pp 236--251 https://dx.doi.org/10.22436/jmcs.038.02.06
Publication Date: December 13, 2024 Submission Date: April 18, 2024 Revision Date: June 30, 2024 Accteptance Date: August 26, 2024

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.


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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


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