Skip to main content
Log in

Nonlinear Riemann-Liouville Fractional Differential Equations With Nonlocal Erdélyi-Kober Fractional Integral Conditions

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

Abstract

In this paper we study a new class of Riemann-Liouville fractional differential equations subject to nonlocal Erdélyi-Kober fractional integral boundary conditions. Existence and uniqueness results are obtained by using a variety of fixed point theorems, such as Banach fixed point theorem, Nonlinear Contractions, Krasnoselskii fixed point theorem, Leray-Schauder Nonlinear Alternative and Leray-Schauder degree theory. Examples illustrating the obtained results are also presented.

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. R.P. Agarwal, Y. Zhou, Y. He, Existence of fractional neutral functional differential equations. Comput. Math. Appl. 59 (2010), 1095–1100.

    Article  MathSciNet  Google Scholar 

  2. B. Ahmad, J.J. Nieto, Boundary value problems for a class of sequential integrodifferential equations of fractional order. J. Funct. Spaces Appl. 2013 (2013) Art. ID 149659, 8 pp.

  3. B. Ahmad, J.J. Nieto, Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions. Bound. Value Probl. 2011 (2011), # 36.

  4. B. Ahmad, S.K. Ntouyas, A. Alsaedi, New existence results for nonlinear fractional differential equations with three-point integral boundary conditions. Adv. Differ. Equ. 2011 (2011) Art. ID 107384 11 pp.

  5. B. Ahmad, S.K. Ntouyas, A. Alsaedi, A study of nonlinear fractional differential equations of arbitrary order with Riemann-Liouville type multistrip boundary conditions. Math. Probl. Eng. 2013 (2013) Art. ID 320415, 9 pp.

  6. B. Ahmad, S.K. Ntouyas, Fractional differential inclusions with fractional separated boundary conditions. Fract. Calc. Appl. Anal. 15, No 3 (2012), 362–382; DOI: 10.2478/s13540-012-0027-y; http://www.degruyter.com/view/j/fca.2012.15.issue-3/issue-files/fca.2012.15.issue-3.xml.

    Article  MathSciNet  Google Scholar 

  7. B. Ahmad, S.K. Ntouyas, A fully Hadamard-type integral boundary value problem of a coupled system of fractional differential equations. Fract. Calc. Appl. Anal. 17, No 2 (2014), 348–360; DOI: 10.2478/s13540-014-0173-5; http://www.degruyter.com/view/j/fca.2014.17.issue-2/issue-files/fca.2014.17.issue-2.xml.

    Article  MathSciNet  Google Scholar 

  8. B. Ahmad, S.K. Ntouyas, Nonlocal fractional boundary value problems with slit-strips integral boundary conditions. Fract. Calc. Appl. Anal. 18, No 1 (2015), 261–280; DOI: 10.1515/fca-2015-0017; http://www.degruyter.com/view/j/fca.2015.18.issue-1/issue-files/fca.2015.18.issue-1.xml.

    Article  MathSciNet  Google Scholar 

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

    Chapter  Google Scholar 

  10. D. Baleanu, O.G. Mustafa, R.P. Agarwal, On Lp-solutions for a class of sequential fractional differential equations. Appl. Math. Comput. 218 (2011), 2074–2081.

    MathSciNet  MATH  Google Scholar 

  11. D.W. Boyd, J.S.W Wong, On nonlinear contractions. Proc. Amer. Math. Soc. 20 (1969), 458–464.

    Article  MathSciNet  Google Scholar 

  12. A. Granas, J. Dugundji, Fixed Point Theory. Springer-Verlag, New York, 2003.

    Book  Google Scholar 

  13. A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations North-Holland Mathematics Studies 204. Elsevier Science B.V, Amsterdam, 2006.

    Google Scholar 

  14. V. Kiryakova, Generalized Fractional Calculus and Applications Pitman Research Notes in Math. 301. Longman, Harlow - J. Wiley, N. York, 1994.

    Google Scholar 

  15. H. Kober, On fractional integrals and derivatives. Quart. J. Math. Oxford Ser. ll (1940), 193–211.

    Article  MathSciNet  Google Scholar 

  16. M.A. Krasnoselskii, Two remarks on the method of successive approximations. Uspekhi Mat. Nauk. 10 (1955), 123–127.

    MathSciNet  Google Scholar 

  17. X. Liu, M. Jia, W. Ge, Multiple solutions of a p-Laplacian model involving a fractional derivative. Adv. Difference Equ. 2013 (2013), # 126.

  18. D. O’Regan, S. Stanek, Fractional boundary value problems with singularities in space variables. Nonlinear Dynam. 71 (2013), 641–652.

    Article  MathSciNet  Google Scholar 

  19. I. Podlubny, Fractional Differential Equations. Academic Press, San Diego, (1999).

    MATH  Google Scholar 

  20. 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 

  21. I.N. Sneddon, The use in mathematical analysis of Erdélyi-Kober operators and some of their applications. Fractional Calculus and Its Applications Proc. Internat. Conf. Held in New Haven, Lecture Notes in Math. 457 Springer, N. York, 1975, 37–79.

    Article  Google Scholar 

  22. S.B. Yakubovich, Yu.F. Luchko, The Hypergeometric Approach to Integral Transforms and Convolutions. Mathematics and its Appl. 287. Kluwer Acad. Publ, Dordrecht-Boston-London, 1994.

    Book  Google Scholar 

  23. L. Zhang, B. Ahmad, G. Wang, R.P. Agarwal, Nonlinear fractional integro-differential equations on unbounded domains in a Banach space. J. Comput. Appl. Math. 249 (2013), 51–56.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Natthaphong Thongsalee.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Thongsalee, N., Ntouyas, S.K. & Tariboon, J. Nonlinear Riemann-Liouville Fractional Differential Equations With Nonlocal Erdélyi-Kober Fractional Integral Conditions. FCAA 19, 480–497 (2016). https://doi.org/10.1515/fca-2016-0025

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1515/fca-2016-0025

MSC 2010

Key Words and Phrases

Navigation