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

Volume 29, Issue 4, pp 369--386 https://doi.org/10.22436/jmcs.029.04.06

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.

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Keywords

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

MSC

•  05A30
•  33D05
•  44A35

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