Journal of applied mathematics & informatics

  • 제41권1호
  • /
  • Pages.83-93
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  • 2023
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  • 2734-1194(pISSN)
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  • 2234-8417(eISSN)
한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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ACCESS TO LAPLACE TRANSFORM OF fg

  • HWAJOON, KIM (Kyungdong University) ;
  • SOMCHAI, LEKCHAROEN (Rangsit University)
  • 투고 : 2022.06.09
  • 심사 : 2022.09.22
  • 발행 : 2023.01.30
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초록

We would like to consider Laplace transform of the form of fg, the form of product, and applies it to Burger's equation in general case. This topic has not yet been addressed, and the methodology of this article is done by considerations with respect to several approaches about the transform of the form of f g and the mean value theorem for integrals. This paper has meaning in that the integral transform method is applied to solving nonlinear equations.

키워드

과제정보

The first author (Hj. Kim) acknowledges the support of Kyungdong University Research Fund, 2022.

참고문헌

  1. R.G. Bartle and D.R. Sherbert, Introduction to real analysis, John Willy & Sons, Inc., New York, 1982.
  2. R.G. Bartle, The elements of integration and Lebesgue measure, John Willy & Sons, Inc., New York, 1995.
  3. F.B.M. Belgacem and S. Sivasundaram, New developments in computational techniques and transform theory applications to nonlinear fractional and stochastic differential equations and systems, Nonlinear Studies 22 (2015), 561-563.
  4. Gj. Han and Hj. Kim, On the Relationship between the Integral of Derivative and the Derivative of the Integral, European J. of Pure and Applied Mathematics 15 (2022), 1211-1216. https://doi.org/10.29020/nybg.ejpam.v15i3.4424
  5. D.L. Cohn, Measure theory, Birkhauser, Boston, 1980.
  6. H. Eltayeb and A. kilicman, On Some Applications of a New Integral Transform, Int. J. of Math. Anal. 4 (2010), 123-132.
  7. Evans, J. David, and A.R. Abdullah, The group explicit method for the solution of Burger's equation, Computing 32 (1984), 239-253. https://doi.org/10.1007/BF02243575
  8. Hj. Kim and Tarig. M. Elzaki, The representation on solutions of Burger's equation by Laplace transform, Int. J. of Math. Anal. 31 (2014), 1543-1548. https://doi.org/10.12988/ijma.2014.46185
  9. T.M. Elzaki, S.M. Ezaki and E.M.A. Hilal, ELzaki and Sumudu Transform for Solving some Differential Equations, Glob. J. of Pure & Appl. Math. 8 (2012), 167-173.
  10. Jy. Jang and Hj. Kim, An application of monotone convergence theorem in PDEs and Fourier analysis, Far East J. Math. Sci. 98 (2015), 665-669.
  11. Hj. Kim, The intrinsic structure and properties of Laplace-typed integral transforms, Mathematical Problem in Engineering 2017 (2017), 1-8.
  12. Hj. Kim, The solution of PDE modeling of semi-infinite string by Elzaki transform, Int. J. Pure & Appl. Math. 111 (2016), 1-8.
  13. Hj. Kim, The time shifting theorem and the convolution for Elzaki transform, Int. J. of Pure & Appl. Math. 87 (2013), 261-271.
  14. Hj. Kim, The solution of the heat equation without boundary conditions, Dynamic Systems and Applications 27 (2018), 653-662.
  15. E. Kreyszig, Advanced Engineering Mathematics, Wiley, Singapore, 2013.
  16. R.I. Nuruddeena, Lawal Muhammadb, A.M. Nassc, T.A. Sulaiman, A Review of the Integral Transforms-Based Decomposition Methods and their Applications in Solving Nonlinear PDEs, Palestine Journal of Mathematics 7 (2018), 262-280.
  17. R.I. Nuruddeena, Y. Akbar, and Hj. Kim, On the application of Gα integral transform to nonlinear dynamical models with non-integer order derivatives, AIMS mathematics 7 (2022), 17859-17878. https://doi.org/10.3934/math.2022984
  18. A.K. Rathie, Yh. Geum, and Hj. Kim, A Note on Certain Laplace Transforms of Convolution-Type Integrals Involving Product of Two Generalized Hypergeometric Functions, Mathematical Problems in Engineering 2021 (2021). https://doi.org/10.1155/2021/8827275
  19. G.K. Watugula, Sumudu Transform: a new integral transform to solve differential equations and control engineering problems, Int. J. of Math. Edu. in Sci. & Tech. 24 (1993), 409-421.