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Operational Method of Solution of some Convolution Equations

  • Semen B. Yakubovich
  • Yurii F. Luchko
Part of the Mathematics and Its Applications book series (MAIA, volume 287)

Abstract

It is well known that the Mikusinski’s operational calculus as well as other operational calculi for hyper-Bessel type differential operators were used for the solution of ordinary differential equations both with constant and variable coefficients and for the solution of some partial differential equations (see, for example, V.A. Ditkin and A.P. Prudnikov (1963), Yu. F. Luchko and S.B. Yakubovich (1993), (1994), N.A. Meller (1960), J. Mikusinski (1959), J. Rodrigues (1989), K. Yosida (1984)). It is worth mentioning that operational method may be used for the solution of integral equations as well. This idea was realized, in particular, in R.G. Buschman (1972), A. Erdelyi (1962), D. Nikolic-Despotovic (1975) for the case of integral equations of the first kind. In this chapter, we will investigate an application of operational calculi developed in the Chapter 19 to the solution of some classes integral equations of the second kind.

Keywords

Integral Equation Unique Solution Operational Calculus Fractional Integration Operator Convolution Equation 
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Copyright information

© Springer Science+Business Media Dordrecht 1994

Authors and Affiliations

  • Semen B. Yakubovich
    • 1
  • Yurii F. Luchko
    • 1
  1. 1.Department of Mathematics and MechanicsBeylorussian State UniversityMinsk, ByelorussiaRussia

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