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On Sumudu transform and system of differential equations. (English) Zbl 1197.34001
Summary: A regular system of differential equations with convolution terms is solved by a special integral transform, the so-called Sumudu transform.

MSC:
34A05Methods of solution of ODE
34C20Transformation and reduction of ODE and systems, normal forms
44A99Miscellaneous topics of integral transforms and operational calculus
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Full Text: DOI
References:
[1] G. K. Watugala, “The Sumudu transform for functions of two variables,” Mathematical Engineering in Industry, vol. 8, no. 4, pp. 293-302, 2002. · Zbl 1025.44003
[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. · Zbl 0768.44003 · doi:10.1080/0020739930240105
[3] S. Weerakoon, “Application of Sumudu transform to partial differential equations,” International Journal of Mathematical Education in Science and Technology, vol. 25, no. 2, pp. 277-283, 1994. · Zbl 0812.35004 · doi:10.1080/0020739940250214
[4] M. A. Asiru, “Sumudu transform and the solution of integral equations of convolution type,” International Journal of Mathematical Education in Science and Technology, vol. 32, no. 6, pp. 906-910, 2001. · Zbl 1008.45003 · doi:10.1080/002073901317147870
[5] A. Kılı\ccman and H. E. Gadain, “An application of double Laplace transform and double Sumudu transform,” Lobachevskii Journal of Mathematics, vol. 30, no. 3, pp. 214-223, 2009. · Zbl 1223.44002 · doi:10.1134/S1995080209030044
[6] F. B. M. Belgacem, “Boundary value problem with indefinite weight and applications,” Problems of Nonlinear Analysis in Engineering Systems, vol. 10, no. 2, pp. 51-58, 1999.
[7] A. Kadem, “Solving the one-dimensional neutron transport equation using Chebyshev polynomials and the Sumudu transform,” Analele Universitatii din Oradea. Fascicola Matematica, vol. 12, pp. 153-171, 2005. · Zbl 1164.82331
[8] H. Eltayeb and A. Kılı\ccman, “On double Sumudu transform and double Laplace transform,” Malaysian Journal of Mathematical Sciences, vol. 4, no. 1, pp. 17-30, 2010.
[9] A. Kılı\ccman and H. Eltayeb, “A note on integral transforms and partial differential equations,” Applied Mathematical Sciences, vol. 4, no. 3, pp. 109-118, 2010. · Zbl 1194.35017 · http://www.m-hikari.com/ams/ams-2010/ams-1-4-2010/index.html
[10] H. Eltayeb and A. Kılı\ccman, “On some applications of a new integral transform,” International Journal of Mathematical Analysis, vol. 4, no. 3, pp. 123-132, 2010. · Zbl 1207.34015 · http://www.m-hikari.com/ijma/ijma-2010/ijma-1-4-2010/index.html