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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 1762729, 8 pages
https://doi.org/10.1155/2017/1762729
Research Article

The Intrinsic Structure and Properties of Laplace-Typed Integral Transforms

Faculty of General Education, Kyungdong University, Yangju, Gyeonggi 11458, Republic of Korea

Correspondence should be addressed to Hwajoon Kim

Received 14 February 2017; Revised 12 April 2017; Accepted 10 May 2017; Published 8 June 2017

Academic Editor: Salvatore Strano

Copyright © 2017 Hwajoon Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. E. Kreyszig, Advanced Engineering Mathematics, Wiley, Singapore, 2013.
  2. G. K. Watugala, “Sumudu transform—a new integral transform to solve differential equations and control engineering problems,” International Journal of Mathematical Education in Science and Technology, vol. 24, no. 1, pp. 35–43, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  3. T. M. Elzaki, S. M. Elzaki, and E. M. A. Hilal, “Elzaki and Sumudu transforms for solving some differential equations,” Global Journal of Pure & Applied Mathematics, vol. 8, no. 2, pp. 167–173, 2012. View at Google Scholar · View at Scopus
  4. Hj. Kim, “The time shifting theorem and the convolution for Elzaki transform,” Global Journal of Pure and Applied Mathematics, vol. 87, pp. 261–271, 2013. View at Google Scholar
  5. F. B. Belgacem and S. Sivasundaram, “New developments in computational techniques and transform theory applications to nonlinear fractional and stochastic differential equations and systems,” Nonlinear Studies. The International Journal, vol. 22, no. 4, pp. 561–563, 2015. View at Google Scholar · View at MathSciNet
  6. F. B. M. Belgacem and A. Karaballi, “Sumudu transform fundamental properties investigations and applications,” Journal of Applied Mathematics and Stochastic Analysis, vol. 2006, Article ID 91083, 23 pages, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. T. M. Elzaki and J. Biazar, “Homotopy perturbation method and Elzaki transform for solving system of nonlinear partial differential equations,” World Applied Sciences Journal, vol. 24, no. 7, pp. 944–948, 2013. View at Publisher · View at Google Scholar · View at Scopus
  8. T. M. Elzaki and H. Kim, “The solution of radial diffusivity and shock wave equations by Elzaki variational iteration method,” International Journal of Mathematical Analysis, vol. 9, no. 21-24, pp. 1065–1071, 2015. View at Publisher · View at Google Scholar · View at Scopus
  9. H. A. Agwa, F. M. Ali, and A. Kilicman, “A new integral transform on time scales and its applications,” Advances in Difference Equations, vol. 60, pp. 1–14, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  10. H. Eltayeb and A. Kilicman, “On some applications of a new integral transform,” International Journal of Mathematical Analysis, vol. 4, no. 1-4, pp. 123–132, 2010. View at Google Scholar · View at MathSciNet
  11. H. Eltayeb, A. Kilicman, and M. B. Jleli, “Fractional Integral Transform and Application,” Abstract and Applied Analysis, vol. 2015, Article ID 150863, 1 page, 2015. View at Publisher · View at Google Scholar
  12. H. Kim, “The form of solution of ODEs with variable coefficients by means of the integral and Laplace transform,” Global Journal of Pure and Applied Mathematics, vol. 12, pp. 2901–2904, 2016. View at Google Scholar
  13. H. Kim, “The shifted data problems by using transform of derivatives,” Applied Mathematical Sciences, vol. 8, no. 149-152, pp. 7529–7534, 2014. View at Publisher · View at Google Scholar · View at Scopus
  14. D. L. Cohn, Measure Theory, Birkhäauser, Boston, Mass, USA, 1980. View at MathSciNet
  15. H. C. Chae and H. Kim, “The validity checking on the exchange of integral and limit in the solving process of PDEs,” International Journal of Mathematical Analysis, vol. 8, no. 22, pp. 1089–1092, 2014. View at Publisher · View at Google Scholar
  16. J. Jang and H. Kim, “An application of monotone convergence theorem in pdes and fourier analysis,” Far East Journal of Mathematical Sciences, vol. 98, no. 5, pp. 665–669, 2015. View at Publisher · View at Google Scholar · View at Scopus