## Tbilisi Mathematical Journal

- Tbilisi Math. J.
- Volume 8, Issue 2 (2015), 1-22.

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

#### Abstract

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 nonlinearities, 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.

#### Article information

**Source**

Tbilisi Math. J., Volume 8, Issue 2 (2015), 1-22.

**Dates**

Received: 14 August 2014

Accepted: 20 September 2014

First available in Project Euclid: 12 June 2018

**Permanent link to this document**

https://projecteuclid.org/euclid.tbilisi/1528769002

**Digital Object Identifier**

doi:10.1515/tmj-2015-0003

**Mathematical Reviews number (MathSciNet)**

MR3323916

**Zentralblatt MATH identifier**

1317.34014

**Subjects**

Primary: 92D25: Population dynamics (general)

Secondary: 34A37: Differential equations with impulses 34K15

**Keywords**

Singular fractional differential system impulsive boundary value problem Riemann-Liouville fractional differential equation with multiple base points fixed point theorem

#### Citation

Liu, Yuji. New results on the existence of solutions of boundary value problems for singular fractional differential systems with impulse effects. Tbilisi Math. J. 8 (2015), no. 2, 1--22. doi:10.1515/tmj-2015-0003. https://projecteuclid.org/euclid.tbilisi/1528769002