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Jan 2017 A survey and new investigation on $(n,n-k)$-type boundary value problems for higher order impulsive fractional differential equations
Yuji Liu
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Tbilisi Math. J. 10(1): 207-248 (Jan 2017). DOI: 10.1515/tmj-2017-0014

Abstract

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.

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Yuji Liu. "A survey and new investigation on $(n,n-k)$-type boundary value problems for higher order impulsive fractional differential equations." Tbilisi Math. J. 10 (1) 207 - 248, Jan 2017. https://doi.org/10.1515/tmj-2017-0014

Information

Received: 10 July 2016; Accepted: 22 August 2016; Published: Jan 2017
First available in Project Euclid: 26 May 2018

zbMATH: 06707546
MathSciNet: MR3630173
Digital Object Identifier: 10.1515/tmj-2017-0014

Subjects:
Primary: 92D25

Rights: Copyright © 2017 Tbilisi Centre for Mathematical Sciences

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Vol.10 • No. 1 • Jan 2017
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