# On a system of $(p,q)$-analogues of the natural transform for solving $(p,q)$-differential equations

Volume 29, Issue 4, pp 369--386
Publication Date: November 24, 2022 Submission Date: July 08, 2022 Revision Date: August 01, 2022 Accteptance Date: August 25, 2022
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### 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. J. Tariboon - Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand. S.K. Ntouyas - Department of Mathematics, University of Ioannina, Ioannina 45110, Greece. Sh. Al-Omari - Faculty of Engineering Technology, Al-Balqa Applied University, Amman 11134, Jordan.

### Abstract

In this work, we apply the concept of $(p,q)$-calculus or post quantum calculus to establish the definitions of $(p,q)$-analogues of the natural transform of the first and second kind, which is a symmetric relation between $(p,q)$-analogues of the natural, Laplace, and Sumudu transforms. Moreover, as a result of the convolution theorem, some properties and some functions present in the table of $(p,q)$-analogues of the natural transform are discussed. Also, we apply them to solve higher order $(p,q)$-IVP with constants and coefficients, and to show the performance and effectiveness of the proposed transform.

### Share and Cite

##### ISRP Style

S. Jirakulchaiwong, K. Nonlaopon, J. Tariboon, S.K. Ntouyas, Sh. Al-Omari, On a system of $(p,q)$-analogues of the natural transform for solving $(p,q)$-differential equations, Journal of Mathematics and Computer Science, 29 (2023), no. 4, 369--386

##### AMA Style

Jirakulchaiwong S., Nonlaopon K., Tariboon J., Ntouyas S.K., Al-Omari Sh., On a system of $(p,q)$-analogues of the natural transform for solving $(p,q)$-differential equations. J Math Comput SCI-JM. (2023); 29(4):369--386

##### Chicago/Turabian Style

Jirakulchaiwong, S., Nonlaopon, K., Tariboon, J., Ntouyas, S.K., Al-Omari, Sh.. "On a system of $(p,q)$-analogues of the natural transform for solving $(p,q)$-differential equations." Journal of Mathematics and Computer Science, 29, no. 4 (2023): 369--386

### Keywords

• $(p,q)$-natural transforms
• $(p,q)$-derivative
• $(p,q)$-integral
• $(p,q)$-calculus
• $(p,q)$-difference equations
• $(p,q)$-convolution theorem

•  05A30
•  33D05
•  44A35