Abstract and Applied Analysis

Solving Fractional Difference Equations Using the Laplace Transform Method

Li Xiao-yan and Jiang Wei

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Abstract

We discuss the Laplace transform of the Caputo fractional difference and the fractional discrete Mittag-Leffer functions. On these bases, linear and nonlinear fractional initial value problems are solved by the Laplace transform method.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 230850, 6 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412273198

Digital Object Identifier
doi:10.1155/2014/230850

Mathematical Reviews number (MathSciNet)
MR3176724

Zentralblatt MATH identifier
07021958

Citation

Xiao-yan, Li; Wei, Jiang. Solving Fractional Difference Equations Using the Laplace Transform Method. Abstr. Appl. Anal. 2014 (2014), Article ID 230850, 6 pages. doi:10.1155/2014/230850. https://projecteuclid.org/euclid.aaa/1412273198


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References

  • I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, Calif, USA, 1999.
    Mathematical Reviews (MathSciNet): MR1658022
  • A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science B.V., Amsterdam, The Netherlands, 2006.
    Mathematical Reviews (MathSciNet): MR2218073
  • V. Lakshmikantham, S. Leela, and J. V. Devi, Theory of Fractional Dynamic Systems, Cambridge Academic Publishers, Cambridge, UK, 2009.
  • K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, NY, USA, 1993.
    Mathematical Reviews (MathSciNet): MR1219954
  • I. Podlubny, A. Chechkin, T. Skovranek, Y. Chen, and B. M. Vinagre Jara, “Matrix approach to discrete fractional calculus. II. Partial fractional differential equations,” Journal of Computational Physics, vol. 228, no. 8, pp. 3137–3153, 2009.
    Mathematical Reviews (MathSciNet): MR2509311
    Zentralblatt MATH: 1160.65308
    Digital Object Identifier: doi:10.1016/j.jcp.2009.01.014
  • M. T. Holm, “The Laplace transform in discrete fractional calculus,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1591–1601, 2011.
    Mathematical Reviews (MathSciNet): MR2824746
    Zentralblatt MATH: 1228.44010
  • T. Abdeljawad, “On Riemann and Caputo fractional differences,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1602–1611, 2011.
    Mathematical Reviews (MathSciNet): MR2824747
    Zentralblatt MATH: 1228.26008
  • F. M. Atici and P. W. Eloe, “Initial value problems in discrete fractional calculus,” Proceedings of the American Mathematical Society, vol. 137, no. 3, pp. 981–989, 2009.
    Mathematical Reviews (MathSciNet): MR2457438
    Zentralblatt MATH: 1166.39005
    Digital Object Identifier: doi:10.1090/S0002-9939-08-09626-3
  • C. S. Goodrich, “Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions,” Computers Mathematics With Applications, vol. 62, pp. 1251–1268, 2011.
    Mathematical Reviews (MathSciNet): MR2754129
  • C. S. Goodrich, “On discrete sequential fractional boundary value problems,” Journal of Mathematical Analysis and Applications, vol. 385, no. 1, pp. 111–124, 2012.
    Mathematical Reviews (MathSciNet): MR2832079
    Zentralblatt MATH: 1236.39008
    Digital Object Identifier: doi:10.1016/j.jmaa.2011.06.022
  • C. S. Goodrich, “Existence of a positive solution to a system of discrete fractional boundary value problems,” Applied Mathematics and Computation, vol. 217, no. 9, pp. 4740–4753, 2011. \endinput
    Mathematical Reviews (MathSciNet): MR2745153
    Zentralblatt MATH: 1215.39003
    Digital Object Identifier: doi:10.1016/j.amc.2010.11.029

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