Have a personal or library account? Click to login
Existence of three positive solutions for boundary value problem with fractional order and infinite delay Cover

Existence of three positive solutions for boundary value problem with fractional order and infinite delay

By: Hedia Benaouda  
Open Access
|Dec 2015

References

  1. [1] Ravi P. Agarwal, Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations., Journal of Mathem. Anal. and Applications, 371, (2010), 57-58.10.1016/j.jmaa.2010.04.034
  2. [2] Ravi P. Agarwal, Boundary value problems for differential equations involving Riemann-Liouville fractional derivative on the half line., Dynamics of Continuous Discrete and Impulsive System, 18, (2011), 235-244.
  3. [3] Zhanbig Bainov, Positive solutions for boundary value problem of nonlinear frac- tional differential equation, Journal of Mathematical Anal and Application, 311, (2005), 495-505.10.1016/j.jmaa.2005.02.052
  4. [4] Ahmad Bachir, Existence of solutions for irregular boundary value problems of nonlinear fractional differential equations, Applied Mathematics Letters, 23, (2010), 390-394.10.1016/j.aml.2009.11.004
  5. [5] Ahmad Bachir, Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions, Boundary Value Problems, 36, (2011), 9 pp.10.1186/1687-2770-2011-36
  6. [6] Jorge Caballero, Positive solutions for a class of singular fractional boundary value problems., Computers Mathematics with Applications, 62, (2011), 1325-1332.10.1016/j.camwa.2011.04.013
  7. [7] Keller Diethelm, On the solution of nonlinear fractional order differential equa- tions used in the modeling of thermoplasticity, in "Scientific Computing in Chemical Engineering II-Computational Fluid Dynamics,Reaction Engineering and Molecular Properties, Springer-Verlag, (1999), 217-224.10.1007/978-3-642-60185-9_24
  8. [8] Jiqin Deng, Existence and uniqueness of solutions of initial value problems for non- linear fractional differential equations, Applied Mathematics Letters, 23, (2010), 676-680.10.1016/j.aml.2010.02.007
  9. [9] Ahmad El Sayed, Nonlinear functional differential equations of arbitrary orders, Nonlinear Analysis, 33, (1998), 181-186.10.1016/S0362-546X(97)00525-7
  10. [10] El Sayed Ahmad, Multivalued fractional differential equations, Applied Mathemat- ical Computation, 68, (1995), 15-25.10.1016/0096-3003(94)00080-N
  11. [11] Dagun Guo, Nonlinear Problems in Abstract Cones, Academic Press, Boston., 1988
  12. [12] Jack Hale, Phase space for retarded equations with infinite delay, Funkcialaj Ekva- cioj, 21, (1978), 11-41.
  13. [13] Yoshiyuki Hino, Functional Differential Equations with Infinite Delay, Springer- Verlag, Berlin, 1991.
  14. [14] Franz Kappel, Some considerations to the fundamental theory of infinite delay equations, Journal of Differential Equations, 37, (1980), 141-183.10.1016/0022-0396(80)90093-5
  15. [15] Ralph Koeller, Application of fractional calculus to the theory of viscolasticity, Journal of Applied Mechanics, 51, (1984), 299-307.10.1115/1.3167616
  16. [16] Nickolai Kosmatov, A singular boundary value problem for nonlinear differential equations of fractional order, Journal of Applied Mathematics and Computing, 28, (2009), 125-135.10.1007/s12190-008-0104-x
  17. [17] Anatoly Kilbas, Theory and Applications of Fractional Differential Equations, El- sevier Science B.V., Amsterdam., 2006
  18. [18] vangipuram Lakshmikantham, Theory of Fractional Dynamic Systems, Cam- bridge Academic Publishers, Cambridge., 2009
  19. [19] Williams Legett, Multiple positive fixed points of nonlinear operators on ordered Banach spaces, Indiana University Mathematics Journal, 428, (1979), 673-688.
  20. [20] Wei Lin, Global existence theory and chaos control of fractional differential equa- tions, Journal of Mathematical Analysis and Applications, 332, (2007), 709-726.10.1016/j.jmaa.2006.10.040
  21. [21] Li Congming, Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations, Computers Mathematics with Applications, 59, (2010), 1363-1375.10.1016/j.camwa.2009.06.029
  22. [22] Yang Liu, A sufficient condition for the existence of a positive solution for a non- linear fractional differential equation with the Riemann Liouville derivative, Applied Mathematics Letters, 25, (2012), 1986-1992.10.1016/j.aml.2012.03.018
  23. [23] Kenneth Miller, An Introduction to the Fractional Calculus and Fractional Differ- ential Equations, Wiley, New York., 1993
  24. [24] Zaid Odibat, An algorithm for the numerical solution of differential equations of fractional order, Journal of Applied Mathematics Informatics, 26, (2008), 15-27.
  25. [25] Igor Podlubny, Geometric and physical interpretation of fractional integration and fractional differentiation, Fractional Calculus and Applied Analysis, 5, (2002), 367-386.
  26. [26] Tingting Qiu, Existence of positive solutions for singular fractional differential equa- tions, Electronic Journal of Differential Equations, (2008), 1-9.
  27. [27] Konrad Schumacher, Existence and continuous dependence for differential equa- tions with unbounded delay, Archive for Rational Mechanics and Analysis, 64, (1978), 315-335.10.1007/BF00247662
  28. [28] Shuqin Zhang, Positive solutions for boundary-value problems of nonlinear frac- tional differential equations, Electron. J. Differential Equations, 36, (2006), 1-12.10.1155/2007/76493
  29. [29] Yige Zhao, Positive Solutions to Boundary Value Problems of Nonlinear Fractional Differential Equations, Applied Mathematics and Computation, (2011), 6950-6958. 10.1016/j.amc.2011.01.103
DOI: https://doi.org/10.1515/awutm-2015-0004 | Journal eISSN: 1841-3307 | Journal ISSN: 1841-3293
Language: English
Page range: 57 - 76
Submitted on: Apr 25, 2015
Accepted on: Jun 29, 2015
Published on: Dec 12, 2015
Published by: West University of Timisoara
In partnership with: Paradigm Publishing Services
Publication frequency: Volume open

© 2015 Hedia Benaouda, published by West University of Timisoara
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.