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Tbilisi Mathematical Journal

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New results on the existence of solutions of boundary value problems for singular fractional differential systems with impulse effects

Yuji Liu
  • Corresponding author
  • Department of Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320, P.R.China
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Published Online: 2015-02-23 | DOI: https://doi.org/10.1515/tmj-2015-0003


Results on the existence of solutions to a new class of impulsive singular fractional differential systems with multiple base points are established. The assumptions imposed on the nonlinear- ities, see ((C) and (D) in Theorem 3.1), are weaker than known ones, (i.e., (A) in Introduction section). The analysis relies on the well known fixed point theorems. An example is given to illustrate the efficiency of the main theorems. The investigation shows that these results and methods are helpful for study in the nonlinear area and the numerical simulation, especially for study in the the numerical solution of a fractional differential equation with multiple base points with or without impulse effects. A section "Conclusions" is given with future work research directions.

Keywords: Singular fractional differential system; impulsive boundary value problem; Riemann-Liouville fractional differen- tial equation with multiple base points; fixed point theorem.


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About the article

Published Online: 2015-02-23

Citation Information: Tbilisi Mathematical Journal, Volume 8, Issue 2, ISSN (Online) 1512-0139, DOI: https://doi.org/10.1515/tmj-2015-0003.

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© 2015 Yuji Liu. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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