Skip to main content
Log in

Regular Fractional Differential Equations in the Sobolev Space

  • Short Paper
  • Published:
Fractional Calculus and Applied Analysis Aims and scope Submit manuscript

Abstract

In this paper regular fractional Sturm-Liouville boundary value problems are considered. In particular, new inner products are described in the Sobolev space and a symmetric operator is established in this space.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. K. Balachandran, S. Divya, M. Rivero, J.J. Trujillo, Controllability of nonlinear implicit neutral fractional Volterra integrodifferential systems. J. Vibr. Contr. 22 (2016), 2165–2172.

    Article  MathSciNet  Google Scholar 

  2. D. Baleanu, K. Diethelm, E. Scalas, J.J. Trujillo, Fractional Calculus Models and Numerical Methods. Ser. on Complexity, Nonlinearity and Chaos, World Scientific (2012).

    Book  Google Scholar 

  3. T. Blaszczyk, M. Cielsieski, Numerical solution of fractional Sturm-Liouville equation in integral form. Fract. Calc. Appl. Anal. 17, No 2 (2014), 307–320; DOI: 10.2478/s13540-014-0170-8; https://www.degruyter.com/view/j/fca.2014.17.issue-2/issue-files/fca.2014.17.issue-2.xml.

    Article  MathSciNet  Google Scholar 

  4. R. Garra, A. Giusti, F. Mainardi, G. Pagnini, Fractional relaxation with time-varying coefficient. Fract. Calc. Appl. Anal. 17, No 2 (2014), 424–439; DOI: 10.2478/s13540-014-0178-0; https://www.degruyter.com/view/j/fca.2014.17.issue-2/issue-files/fca.2014.17.issue-2.xml.

    Article  MathSciNet  Google Scholar 

  5. A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Application of Fractional Differential Equations. Elsevier, Vol. 204, 45–50 (2006).

    Google Scholar 

  6. M. Klimek, O.P. Agrawal, Fractional Sturm-Liouville problem. Comput. Math. Appl. 66 (2013), 795–812.

    Article  MathSciNet  Google Scholar 

  7. M. Klimek, A.B. Malinowska, T. Odzijewicz, Applications of the fractional Sturm-Liouville problem to the space-time fractional diffusion in a finite domain. Fract. Calc. Appl. Anal. 19, No 2 (2016), 516–550; DOI: 10.1515/fca-2016-0027; https://www.degruyter.com/view/j/fca.2016.19.issue-2/issue-files/fca.2016.19.issue-2.xml.

    Article  MathSciNet  Google Scholar 

  8. A.M. Krall, Left definite theory for second order differential operators with mixed boundary conditions. J. Differ. Eqs. 118 (1995), 153–165.

    Article  MathSciNet  Google Scholar 

  9. A.M. Krall, Hilbert Space, Boundary Value Problems and Orthogonal Polynomials. Birkhauser Verlag, Basel (2002).

    Book  Google Scholar 

  10. I. Podlubny, Fractional Differential Equations. Academic Press, New York (1999).

    MATH  Google Scholar 

  11. K.R. Prasad, B.M.B. Brushna, Eigenvalues for iterative systems of Sturm-Liouville fractional order two-point boundary value problems. Fract. Calc. Appl. Anal. 17, No 3 (2014), 638–653; DOI: 10.2478/s13540-014-0190-4; https://www.degruyter.com/view/j/fca.2014.17.issue-3/issue-files/fca.2014.17.issue-3.xml.

    Article  MathSciNet  Google Scholar 

  12. S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives Theory and Applications. Gordon and Breach, New York (1993).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ekin Ugurlu.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ugurlu, E., Baleanu, D. & Tas, K. Regular Fractional Differential Equations in the Sobolev Space. FCAA 20, 810–817 (2017). https://doi.org/10.1515/fca-2017-0041

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1515/fca-2017-0041

MSC 2010

Key Words and Phrases

Navigation