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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:

34A05 | Explicit solutions, first integrals of ordinary differential equations |

34C20 | Transformation and reduction of ordinary differential equations and systems, normal forms |

44A99 | Integral transforms, operational calculus |

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\textit{A. Kiliçman} et al., Abstr. Appl. Anal. 2010, Article ID 598702, 11 p. (2010; Zbl 1197.34001)

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### 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 |

[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 |

[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 |

[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 |

[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 |

[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 |

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