Uniqueness results for nonlinear fractional differential equations with infinite-point integral boundary conditions
-
2176
Downloads
-
3569
Views
Authors
Suli Liu
- Department of Mathematics, Jilin University, Changchun, 130012, P. R. China.
Junpeng Liu
- Department of Mathematics, Jilin University, Changchun, 130012, P. R. China.
Qun Dai
- College of Science, Changchun University of Science and Technology, Changchun, 130022, P. R. China.
Huilai Li
- Department of Mathematics, Jilin University, Changchun, 130012, P. R. China.
Abstract
In this paper, we consider a class of nonlinear fractional differential equations involving the Riemann-Liouville fractional
derivative with infinite-point integral boundary conditions. Our analysis relies on the fixed point index theory and \(u_0\)-positive
operator. An example is given for the illustration of the main work.
Share and Cite
ISRP Style
Suli Liu, Junpeng Liu, Qun Dai, Huilai Li, Uniqueness results for nonlinear fractional differential equations with infinite-point integral boundary conditions, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 3, 1281--1288
AMA Style
Liu Suli, Liu Junpeng, Dai Qun, Li Huilai, Uniqueness results for nonlinear fractional differential equations with infinite-point integral boundary conditions. J. Nonlinear Sci. Appl. (2017); 10(3):1281--1288
Chicago/Turabian Style
Liu, Suli, Liu, Junpeng, Dai, Qun, Li, Huilai. "Uniqueness results for nonlinear fractional differential equations with infinite-point integral boundary conditions." Journal of Nonlinear Sciences and Applications, 10, no. 3 (2017): 1281--1288
Keywords
- Fractional differential equations
- infinite-point integral boundary condition
- \(u_0\)-positive operator
- fixed point index theory.
MSC
References
-
[1]
B. Ahmad, R. P. Agarwal, Some new versions of fractional boundary value problems with slit-strips conditions, Bound. Value Probl., 2014 (2014 ), 12 pages.
-
[2]
A. Atangana, D. Baleanu, New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model, Therm. Sci., 20 (2016), 763–769.
-
[3]
A. Atangana, I. Koca, Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order, Chaos Solitons Fractals, 89 (2016), 447–454.
-
[4]
Y.-J. Cui, Uniqueness of solution for boundary value problems for fractional differential equations, Appl. Math. Lett., 51 (2016), 48–54.
-
[5]
D.-J. Guo, Nonlinear integral equations, Shandong Science and Technology Press, Jinan (1987)
-
[6]
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam (2006)
-
[7]
M. A. Krasnoselskiı, Positive solutions of operator equations, Translated from the Russian by Richard E. Flaherty; edited by Leo F. Boron P. Noordhoff Ltd. Groningen, (1964), 381 pages.
-
[8]
S.-L. Liu, H.-L. Li, Q. Dai, Nonlinear fractional differential equations with nonlocal integral boundary conditions, Adv. Difference Equ., 2015 (2015 ), 11 pages.
-
[9]
S.-L. Liu, H.-L. Li, Q. Dai, J.-P. Liu, Existence and uniqueness results for nonlocal integral boundary value problems for fractional differential equations, Adv. Difference Equ., 2016 (2016 ), 14 pages.
-
[10]
J. Sabatier, O. P. Agrawal, J. A. Tenreiro Machado (Eds.), Advances in fractional calculus, Theoretical developments and applications in physics and engineering, Including papers from the Minisymposium on Fractional Derivatives and their Applications (ENOC-2005) held in Eindhoven, August 2005, and the 2nd Symposium on Fractional Derivatives and their Applications (ASME-DETC 2005) held in Long Beach, CA, September 2005, Springer, Dordrecht (2007)
-
[11]
S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional integrals and derivatives, Theory and applications, Edited and with a foreword by S. M. Nikolskiı, Translated from the 1987 Russian original, Revised by the authors, Gordon and Breach Science Publishers, Yverdon (1993)
-
[12]
W.-Z. Xie, J. Xiao, Z.-G. Luo, Existence of extremal solutions for nonlinear fractional differential equation with nonlinear boundary conditions, Appl. Math. Lett., 41 (2015), 46–51.
-
[13]
X.-Q. Zhang, Positive solutions for a class of singular fractional differential equation with infinite-point boundary value conditions, Appl. Math. Lett., 39 (2015), 22–27.