The solution of convolution-typed Volterra integral equation by G-transform

  • Authors

    • Hwajoon Kim Kyungdong University
    • Kamsing Nonlaopon
    2019-07-06
    https://doi.org/10.14419/ijet.v7i4.26348
  • Volterra integral equation, G-transform, initial value problem

  • Abstract

    We would like to consider the solution of convolution-typed Volterra integral equation by using G-transform, a generalized Laplace-typed transform. The tool of G-transform is analyzed to be well applied to convolution-typed Volterra integral equation.

  • References

    1. 1. 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, Vol. 22 (2015), 561-563.

      2. J. Biazar and K. Hosseini, Analytic approximation of Volterra's population model, J. Appl. Math., Stat. and Infor., Vol. 13 (2017), 5-17.

      3. 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., Vol. 8 (2012), 167-173.

      4. Hj. Kim, The intrinsic structure and properties of Laplace-typed integral transforms, Mathematical Problem in Engineering, Vol. 2017 (2017), 1-8.

      5. Hj. Kim, The time shifting theorem and the convolution for Elzaki transform, Int. J. of Pure & Appl. Math., Vol. 87 (2013), 261-271.

      6. Hj. Kim, The solution of the heat equation without boundary conditions, Dynamic Systems and Applications, Vol. 27 (2018), 653-662.

      7. Hj. Kim, On the form and properties of an integral transform with strength in integral transforms, Far East. J. Math. Sci., Vol. 102, (2017), 2831-2844.

      8. E. Kreyszig, Advanced Engineering Mathematics, Wiley, Singapore, 2013.

      9. R. Medina, Stability for Linear Volterra Difference Equations in Banach Spaces, Abstract and Applied Analysis, Vol. 2018, (2018) 1-7.

      10. S. Sohrabi and H. Ranjbar, On Sinc discretization for systems of Volterra integral-algebraic equations, Applied Mathematics and Computation, Vol. 346 (2019), 193-204.

      11. 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., Vol. 24 (1993), 409-421.

  • Downloads

  • How to Cite

    Kim, H., & Nonlaopon, K. (2019). The solution of convolution-typed Volterra integral equation by G-transform. International Journal of Engineering & Technology, 7(4), 6665-6669. https://doi.org/10.14419/ijet.v7i4.26348

    Received date: 2019-01-22

    Accepted date: 2019-03-29

    Published date: 2019-07-06