DOI QR코드

DOI QR Code

SOLVABILITY OF MULTI-POINT BOUNDARY VALUE PROBLEMS FOR FRACTIONAL DIFFERENTIAL EQUATIONS AT RESONANCE

  • Liu, Yuji (Department of Mathematics Hunan Institute of Science and Technology) ;
  • Liu, Xingyuan (Department of Mathematics Shaoyang University)
  • Published : 2012.08.15

Abstract

Sufficient conditions for the existence of at least one solution of a class of multi-point boundary value problems of the fractional differential equations at resonance are established. The main theorem generalizes and improves those ones in [Liu, B., Solvability of multi-point boundary value problems at resonance(II), Appl. Math. Comput., 136(2003)353-377], see Remark 2.3. An example is presented to illustrate the main results.

Keywords

References

  1. R. P. Agarwal, M. Benchohra, S. Hamani, A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions, Acta Appl Math. 109 (2011), 973-1033.
  2. A. Kilbas, J. Trujillo, Differential equations of fractional order: methods, results and problems-I, Applicable Analysis 78 (2001), 153-192. https://doi.org/10.1080/00036810108840931
  3. K. S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equation, Wiley, New York, 1993.
  4. S. Rida, H. El-Sherbiny, A. Arafa, On the solution of the fractional nonlinear Schrodinger equation, Physics Letters A 372 (2008), 553-558. https://doi.org/10.1016/j.physleta.2007.06.071
  5. S. Samko, A. Kilbas, O. Marichev, Fractional Integral and Derivative, Theory and Applications, Gordon and Breach, 1993.
  6. S. Zhang, The existence of a positive solution for a nonlinear fractional differ- ential equation, J. Math. Anal. Appl. 252 (2000), 804-812. https://doi.org/10.1006/jmaa.2000.7123
  7. E. Kaufmann, E. Mboumi, Positive solutions of a boundary value problem for a nonlinear fractional differential equation, Electronic Journal of Qualitative Theory of Differential Equations 3 (2008), 1-11.
  8. R. Dehghant, K. Ghanbari, Triple positive solutions for boundary value problem of a nonlinear fractional differential equation, Bulletin of the Iranian Mathematical Society 33 (2007), 1-14.
  9. B. Liu, J. Yu, Solvability of multi-point boundary value problems at reso- nance(I), Applied Mathematics and Computation 129 (2002), 119-143. https://doi.org/10.1016/S0096-3003(01)00036-4
  10. B. Liu, Solvability of multi-point boundary value problems at resonance(II), Appl. Math. Comput. 136 (2003), 353-377. https://doi.org/10.1016/S0096-3003(02)00050-4
  11. J. Mawhin, Topological degree methods in nonlinear boundary value problems, in: NSFCBMS Regional Conference Series in Math., American Math. Soc. Providence, RI, 1979.