FURTHER PROPERTIES OF LAPLACE-TYPE INTEGRAL TRANSFORMS

TitleFURTHER PROPERTIES OF LAPLACE-TYPE INTEGRAL TRANSFORMS
Publication TypeJournal Article
Year of Publication2019
AuthorsSATTASO SUPAKNAREE, NONLAOPON KAMSING, KIM HWAJOON
JournalDynamic Systems and Applications
Volume28
Issue1
Start Page195
Pagination22
Date Published01/2019
ISSN1056-2176
AMS Subject Classification34A25, 34A35, 44A05, 44A10, 44A20
Abstract

In this paper, we study some properties of Laplace-type integral transforms, which have been introduced as a computational tool for solving differential equations, and present some examples to illustrate the effectiveness of its applicability. Moreover, we give an example that cannot be solved by Laplace, Sumudu, and Elzaki transforms, but it can be solved by Laplace-type integral transforms; this means
that Laplace-type integral transforms are a powerful tool for solving some differential equations with variable coefficients.

PDFhttps://acadsol.eu/dsa/articles/28/1/12.pdf
DOI10.12732/dsa.v28i1.12
Refereed DesignationRefereed
Full Text

[1] J. E. Hofmann, Leibniz in Paris 1672-1676: His Growth to Mathematical Maturity, Cambridge University Press, Cambridge (1974).
[2] G. K.Watugala, Sumudu transform: a new integral transform to solve differential equations and control engineering problems, Internat. J. Math. Ed. Sci. Tech., 24 (1993), 35-43.
[3] H. ELtayeb and A. Kilicman, On some applications of a new integral transform, Int. J. Math. Anal., 4 (2010), 123-132.
[4] T. M. Elzaki and S. M. Elzaki, On the connections between Laplace and Elzaki transforms, Adv. Theor. Appl. Math., 6 (2011), 1-11.
[5] H. A. Agwa, F. M. Ali, and A. Kilicman, A new integral transform on time scales and its applications, Adv. Difference Equ., 60 (2012), 1-14.
[6] H. Bulut, H. M. Baskonus, and S. Tuluce, The solutions of partial differential equations with variable coefficient by Sumudu transform method, AIP Conf. Proc., 1493 (2012), 91-95, doi: 10.1063/1.4765475.
[7] T. M. Elzaki, S. M. Elzaki, and E. A. Elnour, On the new integral transform Elzaki transform fundamental properties investigation and applications, Glob. J. Math. Sci., 4 (2012), 1-13.
[8] T. M. Elzaki, S. M. Elzaki, and E. M. A. Hilal, Elzaki and Sumudu transforms for solving some differential equations, Glob. J. Pure Appl. Math., 8 (2012), 167-173.
[9] E. Kreyszig, Advanced Engineering Mathematics, Wiley, Singapore (2013).
[10] Hj. Kim, The time shifting theorem and the convolution for Elzaki transform, Glob. J. Pure Appl. Math., 87 (2013), 261-271.
[11] Hj. Kim, The shifted data problems by using transform of derivatives, Appl. Math. Sci., 8 (2014), 7529-7534.
[12] Yc. Song and Hj. Kim, The Solution of Volterra integral equation of the second kind by using the Elzaki transform, Appl. Math. Sci., 8 (2014), 525-530.
[13] 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.
[14] Shendkar Archana M. and Jadhav Pratibha V., Elzaki transform: a solution of differential equations, Int. J. Sci. Eng. Tech. Res., 4 (2015), 1006-1008.
[15] M. Osman, and M. A. Bashir, Solution of partial differential equations with variables coefficients using double Sumudu transform, Int. J. Sci. Res. Publ., 6 (2016), 37-46.
[16] A. Devi, P. Roy and V. Gill, Solution of ordinary differential equations with variable coefficients using Elzaki transform, Asian J. Appl. Sci. Tech., 1 (2017), 186-194.
[17] Hj. Kim, The intrinsic structure and properties of Laplace-typed integral transforms, Math. Probl. Eng., 2017 (2017), Article ID 1762729, 8 pages.
[18] Hj. Kim, On the form and properties of an integral transform with strength in integral transforms, Far East J. Math. Sci., 102 (2017), 2831-2844.
[19] Hj. Kim, The solution of Laguerre’s equation by using G-transform, Int. J. Appl. Eng. Res., 12 (2017), 16083-16086.
[20] R. P. Kanwal, Generalized Functions: Theory and Applications, third edition, Birkhauser, Boston (2004).
[21] J. L. Schiff, The Laplace Transform: Theory and Applications, Springer-Verlag, New York (1999).
[22] H. Eltayeb and A. Kilicman, A note on the Sumudu transforms and differential equations, Appl. Math. Sci., 4 (2010), 1089-1098.