Tbilisi Mathematical Journal
- Tbilisi Math. J.
- Volume 10, Issue 1 (2017), 207-248.
A survey and new investigation on $(n,n-k)$-type boundary value problems for higher order impulsive fractional differential equations
A survey for studies on boundary value problems of higher order ordinary differential equations is given firstly. Secondly a simple review for studies on solvability of boundary value problems for impulsive fractional differential equations is presented. Thirdly by using a general method for converting an impulsive fractional differential equation with the Riemann-Liouville fractional derivatives to an equivalent integral equation and employing fixed point theorems in Banach space, we establish existence results of solutions for three classes of boundary value problems ($(n,n-k)$ type BVPs) of impulsive higher order fractional differential equations. Some examples are presented to illustrate the efficiency of the results obtained and some mistakes are also corrected at the end of the paper finally. A conclusion section is given at the end of the paper.
Tbilisi Math. J., Volume 10, Issue 1 (2017), 207-248.
Received: 10 July 2016
Accepted: 22 August 2016
First available in Project Euclid: 26 May 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 92D25: Population dynamics (general)
Secondary: 34A37: Differential equations with impulses 34K15 34K37: Functional-differential equations with fractional derivatives 34K45: Equations with impulses 34B37: Boundary value problems with impulses 34B15: Nonlinear boundary value problems 34B10: Nonlocal and multipoint boundary value problems 92D25: Population dynamics (general) 34A37: Differential equations with impulses 34K15
Liu, Yuji. A survey and new investigation on $(n,n-k)$-type boundary value problems for higher order impulsive fractional differential equations. Tbilisi Math. J. 10 (2017), no. 1, 207--248. doi:10.1515/tmj-2017-0014. https://projecteuclid.org/euclid.tbilisi/1527300027