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.
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.
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
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
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