Skip to main content

Calculus on Mixed Time Scales

  • Chapter
  • First Online:
  • 2492 Accesses

Abstract

This chapter focuses on what we call the calculus on a mixed time scale whose elements we will define in terms of a point α and two linear functions. There has been recent interest in mixed time scales by Auch [37, 38], Auch et al. [39], Estes [34, 78], Erbe et al. [76], and Mert [145].

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   69.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Bibliography

  1. Atici, F.M., Eloe, P.W.: Initial value problems in discrete fractional calculus. Proc. Am. Math. Soc. 137, 981–989 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  2. Auch, T.: Developement and application of difference and fractional calculus on discrete time scales. PhD Disertation, University of Nebraska-Lincoln (2013)

    Google Scholar 

  3. Auch, T., Lai, J., Obudzinski, E., Wright, C.: Discrete q-calculus and the q-Laplace transform. Panamer. Math. J. 24, 1–19 (2014)

    MathSciNet  MATH  Google Scholar 

  4. Auch, T.: Discrete calculus on a scaled number line. Panamer. Math. J., to appear

    Google Scholar 

  5. Erbe, L., Mert, R., Peterson, A., Zafer, A.: Oscillation of even order nonlinear delay dynamic equations on time scales. Czech. Math. J. 63, 265–279 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  6. Estes, A.: Discrete calculus. Undergraduate Honors Thesis, University of Nebraska-Lincoln, 2013

    Google Scholar 

  7. Kelley, W.G., Peterson, A.C.: The Theory of Differential Equations: Classical and Qualitative, Second Edition. Universitext, Springer, New York (2010)

    Book  Google Scholar 

  8. Mert, R.: Oscillation of higher-order neutral dynamic equations on time scales. Adv. Differ. Equ. (68), 11 pp. (2012)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Goodrich, C., Peterson, A.C. (2015). Calculus on Mixed Time Scales. In: Discrete Fractional Calculus. Springer, Cham. https://doi.org/10.1007/978-3-319-25562-0_5

Download citation

Publish with us

Policies and ethics