# Uniqueness results for nonlinear fractional differential equations with infinite-point integral boundary conditions

Volume 10, Issue 3, pp 1281--1288
Publication Date: March 20, 2017 Submission Date: January 17, 2017
• 1138 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.

•  26A33
•  34A34

### 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.