Skip to main content
SpringerLink
Log in

Fractional Differential Equations

  • Chapter
  • First Online:
Introduction to Fractional Differential Equations

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 25))

Abstract

Let the fractional differential equation (FDE) be

$$\displaystyle (D^\alpha _{a_+}y)(t) = f[t,y(t)],\hspace {0.2 cm} \alpha > 0,\hspace {0.2 cm} t > a,$$

with the conditions:

$$\displaystyle (D^{\alpha - k}_{a+}y)(a+) = b_k,\hspace {0.2 cm} k = 1,\ldots , n,$$

called also Riemann–Liouville FDE.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
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

Notes

  1. 1.

    V. Voltera (1860–1940).

  2. 2.

    P.L. Chebyshev (1821–1894).

  3. 3.

    R.O.S. Lipschitz (1832–1903).

  4. 4.

    E. Picard (1856–1941).

  5. 5.

    G. Adomian (1922–1996).

  6. 6.

    I.M. Ghelfand (1913–2009).

References

  1. Adomian, G. (1988). A review of the decomposition method in applied mathematics. Journal of Mathematical Analysis and Applications, 135(2), 501–544.

    Article  MathSciNet  Google Scholar 

  2. Adomian, G. (1994). Solving frontier problems of physics: The decomposition method. Fundamental theories of physics. Dordrecht: Springer.

    MATH  Google Scholar 

  3. Cherruault, Y. (1989). Convergence of Adomian’s method. Kybernetes, 18(2), 31–38.

    Article  MathSciNet  Google Scholar 

  4. El’sgol’ts, L. E., & Norkin, S. B. (1973). Introduction to the theory of differential equations with deviating arguments. Mathematics in science and engineering. New York: Academic Press.

    MATH  Google Scholar 

  5. Kazem, S. (2013). Exact solution of some linear differential equations by Laplace transform. International Journal of Nonlinear Science, 16, 3–11.

    MathSciNet  MATH  Google Scholar 

  6. Khan, M., Hussain, M., Jafari, H., & Khan, Y. (2010). Application of Laplace decomposition method to solve nonlinear coupled partial differential equations. World Applied Sciences Journal, 9, 13–19.

    Google Scholar 

  7. Khelifa, S., & Cherruault, Y. (2000). New results for the Adomian method. Kybernetes, 29, 332–354.

    Article  MathSciNet  Google Scholar 

  8. Milici, C., & Drăgănescu, G. (2014). A method for solve the nonlinear fractional differential equations. Saarbrücken: Lambert Academic Publishing.

    MATH  Google Scholar 

  9. Natanson, I. P. (1950). Teoria funcţii vescestvennoi peremennoi. Gosudarstvennoe izdatelstvo tehniko-teoreticekoi literaturi, Moscva.

    Google Scholar 

  10. Pinkus, A. (2000). Weierstrass and approximation theory. Journal of Approximation Theory, 107, 1–66.

    Article  MathSciNet  Google Scholar 

  11. O’Shaughnessy, L. (1918). Problem 433. The American Mathematical Monthly, 25, 172.

    Article  MathSciNet  Google Scholar 

  12. Weilbeer, M. (2005). Efficient numerical methods for fractional differential equations and their analytical background. PhD thesis, Facultät für Mathematik und Informatik, Technischen Univerisität Braunschweig, Braunschweig.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Polytechnic University of Timişoara, Timişoara, Romania

    Constantin Milici

  2. Research Center in Theoretical Physics, West University of Timişoara, Timişoara, Romania

    Gheorghe Drăgănescu

  3. Department of Electrical Engineering, Polytechnic of Porto, Porto, Portugal

    J. Tenreiro Machado

Authors
  1. Constantin Milici
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gheorghe Drăgănescu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. Tenreiro Machado
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Milici, C., Drăgănescu, G., Tenreiro Machado, J. (2019). Fractional Differential Equations. In: Introduction to Fractional Differential Equations. Nonlinear Systems and Complexity, vol 25. Springer, Cham. https://doi.org/10.1007/978-3-030-00895-6_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-00895-6_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-00894-9

  • Online ISBN: 978-3-030-00895-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation