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Integral Transforms and Special Functions Volume 24, 2013 - Issue 4
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Original Articles

Further properties of the Laplace transform on time scales with arbitrary graininess

Martin Bohner Department of Mathematics and Statistics, Missouri S&T, Rolla, MO, 65409-0020, USACorrespondence[email protected]
,
Gusein Sh. Guseinov Department of Mathematics, Atilim University, 06836, Incek, Ankara, Turkey
&
Başak Karpuz Department of Mathematics, Afyon Kocatepe University, 03200, Afyonkarahisar, Turkey
Pages 289-301 | Received 07 Mar 2012, Accepted 25 Apr 2012, Published online: 25 Jun 2012

References

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  • Bohner , M. and Guseinov , G. Sh. 2010 . The h-Laplace and q-Laplace transforms . J. Math. Anal. Appl. , 365 ( 1 ) : 75 – 92 . (doi:10.1016/j.jmaa.2009.09.061)
  • Bohner , M. and Guseinov , G. Sh. 2010 . The Laplace transform on isolated time scales . Comput. Math. Appl. , 60 ( 6 ) : 1536 – 1547 . (doi:10.1016/j.camwa.2010.06.037)
  • Bohner , M. , Guseinov , G. Sh. and Karpuz , B. 2011 . Properties of the Laplace transform on time scales with arbitrary graininess . Integ. Trans. Spec. Funct. , 22 ( 11 ) : 785 – 800 . (doi:10.1080/10652469.2010.548335)
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  • Davis , J. M. , Gravagne , I. A. , Jackson , B. J. , Marks Ii , R. J. and Ramos , A. A. 2007 . The Laplace transform on time scales revisited . J. Math. Anal. Appl. , 332 ( 2 ) : 1291 – 1307 . (doi:10.1016/j.jmaa.2006.10.089)
  • Guseinov , G. Sh. 2003 . Integration on time scales . J. Math. Anal. Appl. , 285 : 107 – 127 . (doi:10.1016/S0022-247X(03)00361-5)
  • Hilger , S. 1990 . Analysis on measure chains – a unified approach to continuous and discrete calculus . Results Math. , 18 : 18 – 56 .
  • Hilger , S. 1999 . Special functions, Laplace and Fourier transform on measure chains . Dynam. Syst. Appl. , 8 ( 3–4 ) : 471 – 488 . Special Issue on “Discrete and continuous hamiltonian systems”, edited by R. P. Agarwal and M. Bohner.
  • Karpuz , B. Unbounded oscillation of higher-order nonlinear delay dynamic equations of neutral type with oscillating coefficients . Electron. J. Qual. Theory Differ. Equ. , 2009 ( 34 ) 1 – 14 .
  • Karpuz , B. 2011 . On uniqueness of the Laplace transform on time scales . Panamer. Math. J. , 21 ( 2 ) : 101 – 110 .
  • Schiff , J. L. 1999 . The Laplace Transform: Theory and Applications , New York : Springer-Verlag . Undergraduate Texts in Mathematics

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