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A survey and new investigation on $(n,n-k)$-type boundary value problems for higher order impulsive fractional differential equations
- Source :
- Tbilisi Math. J. 10, iss. 1 (2017), 207-248
- Publication Year :
- 2017
- Publisher :
- Tbilisi Centre for Mathematical Sciences, 2017.
-
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.
- Subjects :
- Banach space
Fixed-point theorem
fixed point theorem
Riemann-Liouville fractional derivative
92D25
01 natural sciences
34K15
34K37
higher order fractional differential system
Simple (abstract algebra)
Order (group theory)
Boundary value problem
0101 mathematics
Mathematics
34B10
010102 general mathematics
Mathematical analysis
34B37
34B15
Integral equation
34A37
Fractional calculus
010101 applied mathematics
Ordinary differential equation
impulse effect
34K45
$(n,n-k)$ focal boundary value problem
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Tbilisi Math. J. 10, iss. 1 (2017), 207-248
- Accession number :
- edsair.doi.dedup.....2af4b9bcdc169d05adbe2b0765d214b7