
AIMS Mathematics, 2019, 4(3): 880895. doi: 10.3934/math.2019.3.880
Research article
Export file:
Format
 RIS(for EndNote,Reference Manager,ProCite)
 BibTex
 Text
Content
 Citation Only
 Citation and Abstract
Existence of positive solution to the boundary value problems for coupled system of nonlinear fractional differential equations
1 Department of Mathematics, Islamic University, Kushtia7003, Bangladesh
2 Department of Mathematics, University of Rajshahi, Rajshahi6205, Bangladesh
Received: , Accepted: , Published:
References
1. K. Diethelm, The Analysis of Fractional Differential Equations, Springer, 2010.
2. J. Sabatier, O. P. Agrawal, and J. A. T. Machado, Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, 2007.
3. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Vol. 204 of NorthHolland Mathematics Studies, Elsevier Science Limited, 2006.
4. I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.
5. K. S. Miller and B. Ross, An introduction to the fractional calculus and differential equations, John Wiley, New York, 1993.
6. N. Heymans and I. Podlubny, Physical interpretation of initial conditions for fractional differential equations with RiemannLiouville fractional derivatives, Rheol. Acta, 45 (2006), 765771.
7. Q. Sun, H. Ji and Y. Cui, Positive Solutions for Boundary Value Problems of Fractional Differential Equation with Integral Boundary Conditions, J. Funct. Space. Appl., 2018 (2018), 16.
8. W. Ma, S. Meng and Y. Cui, Resonant Integral Boundary Value Problems for Caputo Fractional Differential Equations, Math. Probl. Eng., 2018 (2018), 18.
9. Y. Cu, W. Ma, Q. Sun, et al. New uniqueness results for boundary value problem of fractional differential equation, Nonlinear AnalModel, 23 (2018), 3139.
10. X. Han and X. Yang, Existence and multiplicity of positive solutions for a system of fractional differential equation with parameters, Bound. Value Probl., 2017 (2017), 78.
11. Y. Cui, Q. Sun and X. Su, Monotone iterative technique for nonlinear boundary value problems of fractional order p∈ (2 ,3], Adv. Differ. EquNY, 2017 (2017), 248.
12. T. Qi, Y. Liu and Y. Cui, Existence of Solutions for a Class of Coupled Fractional Differential Systems with Nonlocal Boundary Conditions, J. Funct. Space. Appl., 2017 (2017), 19.
13. T. Qi, Y. Liu and Y. Zou, Existence result for a class of coupled fractional differential systems with integral boundary value conditions, J. Nonlinear Sci. Appl., 10 (2017), 40344045.
14. T. Bashiri, S. M. Vaezpour and C. Park, A coupled fixed point theorem and application to fractional hybrid differential problems, Fixed Point Theory and Applications, 2016 (2016), 23.
15. B. Zhu, L. Liu, and Y. Wu, Local and global existence of mild solutions for a class of nonlinear fractional reactiondiffusion equations with delay, Appl. Math. Lett., 61 (2016), 7379.
16. Y. Wang, L. Liu, X. Zhang, et al. Positive solutions of an abstract fractional semipositone differential system model for bioprocesses of HIV infection, Appl. Math. Comput., 258 (2015), 312324.
17. D. Luo and Z. Luo, Existence and finitetime stability of solutions for a class of nonlinear fractional differential equations with timevarying delays and noninstantaneous impulses, Adv. Differ. EquNY, 2019 (2019), 155.
18. D. Luo, and Z. Luo, Uniqueness and Novel FiniteTime Stability of Solutions for a Class of Nonlinear Fractional Delay Difference Systems, Discrete Dyn. Nat. Soc., 2018 (2018), 17.
19. P. Agarwal, M. Chand, D. Baleanu, et al. On the solutions of certain fractional kinetic equations involving kMittagLeffler function, Adv. Differ. EquNY, 2018 (2018), 249.
20. P. Agarwal, M. Chand, J. Choi, et al. Certain fractional integrals and image formulas of generalized kBessel function, Communications of the Korean Mathematical Society, 33 (2018), 423436.
21. P. Agarwal, A.A. ElSayed, Nonstandard finite difference and Chebyshev collocation methods for solving fractional diffusion equation, Physica A, 500 (2018), 4049.
22. K. Shah, R. A. Khan, Existence and uniqueness of positive solutions to a coupled system of nonlinear fractional order differential equations with antiperiodic boundary conditions, Differ. Equ. Appl., 7 (2015), 245262.
23. M. Hao and C. Zhai, Application of Schauder fixed point theorem to a coupled system of differential equations of fractional order, J. Nonlinear Sci. Appl., 7 (2014), 131137.
24. Y. Cui, Y. Zou, Existence results and the monotone iterative technique for nonlinear fractional differential systems with coupled fourpoint boundary value problems, Abstr. Appl. Anal., 2014 (2014), 16.
25. M. J. Li, Y. L. Liu, Existence and uniqueness of positive solutions for a coupled system of nonlinear fractional differential equations, Open Journal of Applied Sciences, 3 (2013), 5361.
26. C. S. Goodrich, Existence of a positive solution to systems of differential equations of fractional order, Comput. Math. Appl., 62 (2011), 12511268.
27. C. S. Goodrich, Existence of a positive solution to a class of fractional differential equations, Appl. Math. Lett., 23 (2010), 10501055.
28. X. Su, Boundary value problem for a coupled system of nonlinear fractional differential equations, Appl. Math. Lett., 22 (2009), 6469.
29. D. R. Dunninger and H. Y. Wang, Existence and multiplicity of positive solutions for elliptic systems, Nonlinear AnalTheor, 29 (1997), 10511060.
30. J. Leray, J. Schauder, Topologie et equations fonctionels, Ann. Sci. École Norm. Sup., 51 (1934), 4578.
31. M. Fréchet, Sur quelques points du calculfonctionnel, Rend. Circ. Mat. Palermo, 22 (1906), 174.
© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)