Skip to main content

Introduction to Class of Uniformly Fractional Differentiable Functions

  • Conference paper
  • First Online:
Mathematical Modelling, Applied Analysis and Computation (ICMMAAC 2018)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 272))

  • 536 Accesses

Abstract

In this paper, authors introduced new concept of uniformly fractional differentiable functions on an arbitrary interval I of R by using Caputo-type fractional derivative instead of the commonly used first-order derivative. Their interesting properties with few illustrations have been discussed in this paper.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
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

Institutional subscriptions

References

  1. Patel, M.R.: Uniformly differentiable functions. M.Sc. Research Project, Sardar Patel University, 2009–10

    Google Scholar 

  2. Apostol, T.M.: Mathematical Analysis, 2nd edn. Narosa Publishing House (1997)

    Google Scholar 

  3. Caputo, M.: Linear models of dissipation whose \(Q\) is almost frequency independent II. Geophys. J. R. Astron. Soc. 13, 529–539 (1967)

    Google Scholar 

  4. Diethelm, K.: The mean value theorems and a Nagumo-type uniquness theorem for Caputo’s fractional calculus. Fract. Calc. Appl. Anal. 15(2) (2012)

    Google Scholar 

  5. Yang, X.J.: A short note on local fractional calculus of functions of one variable. J. Appl. Libr. Inf. Sci. (JALIS) 1(1), 1–12 (2012)

    Google Scholar 

  6. Yang, X.J., Gao, G.: The fundamentals of local fractional derivative of the one-variable non-differentiable functions. World Sci-Tech. R and D 31(5), 920–921 (2009)

    Google Scholar 

  7. Prajapati, J.C., Kachhia, K.B.: Functions of bounded fractional differential variation a new concept. Georgian Math. J. 23(3), 417–427 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  8. Gilberg, D., Trudinger, N.S.: Elliptic Partial Differential Equations of Second Order. Springer, New York (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jyotindra C. Prajapati .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Kachhia, K.B., Prajapati, J.C. (2019). Introduction to Class of Uniformly Fractional Differentiable Functions. In: Singh, J., Kumar, D., Dutta, H., Baleanu, D., Purohit, S. (eds) Mathematical Modelling, Applied Analysis and Computation. ICMMAAC 2018. Springer Proceedings in Mathematics & Statistics, vol 272. Springer, Singapore. https://doi.org/10.1007/978-981-13-9608-3_6

Download citation

Publish with us

Policies and ethics