Year 2020,
Volume: 69 Issue: 2, 1345 - 1355, 31.12.2020
Songul Batik
,
Fulya Yoruk Deren
References
- Bai, Z., Sun,W., Existence and multiplicity of positive solutions for singular fractional boundary value problems, Comput. Math. Appl., 63 (2012), 1369-1381.
- He, J., Jia, M., Liu, X., Chen, H., Existence of positive solutions for a high order fractional differential equation integral boundary value problem with changing sign nonlinearity, Advances in Difference Equations, (2018) 2018:49.
- Goodrich, C.S., On a fractional boundary value problem with fractional boundary conditions, Appl. Math. Lett., 25 (2012), 1101-1105.
- Goodrich, C.S., Existence of a positive solution to a class of fractional differential equations, Appl. Math. Lett. (2010) 23:1050-1055
- Ahmad, B., Nieto J.J., Alsaedi A., Aqlan, M.H., A Coupled System of Caputo-Type Sequential Fractional Differential Equations with Coupled (Periodic/Anti-periodic Type) Boundary Conditions, Mediterr. J. Math. (2017) 14:227.
- Henderson, J., Luca, R., Positive solutions for a system of nonlocal fractional boundary value problems, Fractional Calculus and Applied Analysis, 16(4) (2013), 985-1008.
- Henderson, J., Luca, R., Systems of Riemann-Liouville fractional equations with multi-point boundary conditions, Applied Mathematics and Computation, 309 (2017), 303-323.
- Henderson, J. and Luca, R. : Positive solutions for a system of semipositone coupled fractional boundary value problems, Boundary Value Problems (2016), 2016:61
- Kilbas, A.A., Srivastava, H.M., Trujillo, J.J., Theory and applications of fractional differential equations, in: North-Holland Mathematics Studies, vol.204, Elsevier Science B.V, Amsterdam, 2006.
- Liu, Y., New existence results for positive solutions of boundary value problems for coupled systems of multi-term fractional differential equations, Hacettepe Journal of Mathematics and Statistics, 45(2) (2016), 391-416.
- Xie, S., Xie, Y., Positive solutions of higher order nonlinear fractional differential systems with nonlocal boundary conditions, Journal of Applied Analysis and Computation, 6(4), (2016), 1211-227.
- Podlubny, I., Fractional Differential Equations, Academic Press, San Diego, 1999.
- Su, X., Boundary value problem for a coupled system of nonlinear fractional differential equations, Applied Mathematics Letters, 22 (2009), 64-69.
- Wang, Y., Positive solutions for a system of fractional integral boundary value problem, Boundary Value Problems, (2013), 2013:256.
- Cabrera, I., Harjani, J., Sadarangani, K., Existence and uniqueness of solutions for a boundary value problem of fractional type with nonlocal integral boundary conditions in Holder spaces, Mediterr. J. Math., (2018), 15-98.
- He, J., Zhang, X., Liu, L., Wu, Y., Cui, Y., Existence and asymptotic analysis of positive solutions for a singular fractional differential equation with nonlocal boundary conditions, Boundary Value Problems, (2018), 2018:189.
- Wang, Y., Liang, S., Wang, Q., Existence results for fractional differential equations with integral and multi-point boundary conditions, Boundary Value Problems, (2018), 2018:4.
- Avery, R.I., Peterson, A.C., Three positive fixed points of nonlinear operators on ordered Banach spaces, Comput. Math. Appl. 42 (2001), 313-322.
- Shah, K., Khan, R. A., Multiple positive solutions to a coupled systems of nonlinear fractional differential equations, Springer Plus, (2016), 5:1116.
- Li, C.F., Luo, X.N., Zuhou, Y., Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations, Computers and Mathematics with Applications 59 (2010), 1363-1375.
- Jiang, J., Wang, H., Existence and uniqueness of solutions for a fractioanl differential equation with multi-point boundary value problems, Journal of Applied Analysis and Computation, 9(6) (2019), 2156-2168.
- Ali, A., Samet, B., Shah, K., Khan, R.A., Existence and stability of solution to a toppled systems of differential equations of non-integer order, Boundary Value Problems, (2017), 2017:16.
- Shah, K., Nonlocal boundary value problems for nonlinear toppled system of fractional differential equations, Hacettepe Journal of Mathematics and Statistics, 49 (1) (2020).
- Shah, K., Khan, R.A., Iterative scheme for a coupled system of fractional-order differential equations with three-point boundary conditions, Mathematical Methods in the Applied Sciences, 41(3) (2018), 1047-1053.
- Shah, K., Zeb, S., Khan, R.A., Multiplicity results of multi-point boundary value problem of nonlinear fractional differential equations, Appl. Math. Inf. Sci., 12(3) (2018), 1-8.
Analysis of fractional differential systems involving Riemann Liouville fractional derivative
Year 2020,
Volume: 69 Issue: 2, 1345 - 1355, 31.12.2020
Songul Batik
,
Fulya Yoruk Deren
Abstract
This paper is devoted to studying the multiple positive solutions for a system of nonlinear fractional boundary value problems. Our analysis is based upon the Avery Peterson fixed point theorem. In addition, we include an example for the demonstration of our main result. .
.
References
- Bai, Z., Sun,W., Existence and multiplicity of positive solutions for singular fractional boundary value problems, Comput. Math. Appl., 63 (2012), 1369-1381.
- He, J., Jia, M., Liu, X., Chen, H., Existence of positive solutions for a high order fractional differential equation integral boundary value problem with changing sign nonlinearity, Advances in Difference Equations, (2018) 2018:49.
- Goodrich, C.S., On a fractional boundary value problem with fractional boundary conditions, Appl. Math. Lett., 25 (2012), 1101-1105.
- Goodrich, C.S., Existence of a positive solution to a class of fractional differential equations, Appl. Math. Lett. (2010) 23:1050-1055
- Ahmad, B., Nieto J.J., Alsaedi A., Aqlan, M.H., A Coupled System of Caputo-Type Sequential Fractional Differential Equations with Coupled (Periodic/Anti-periodic Type) Boundary Conditions, Mediterr. J. Math. (2017) 14:227.
- Henderson, J., Luca, R., Positive solutions for a system of nonlocal fractional boundary value problems, Fractional Calculus and Applied Analysis, 16(4) (2013), 985-1008.
- Henderson, J., Luca, R., Systems of Riemann-Liouville fractional equations with multi-point boundary conditions, Applied Mathematics and Computation, 309 (2017), 303-323.
- Henderson, J. and Luca, R. : Positive solutions for a system of semipositone coupled fractional boundary value problems, Boundary Value Problems (2016), 2016:61
- Kilbas, A.A., Srivastava, H.M., Trujillo, J.J., Theory and applications of fractional differential equations, in: North-Holland Mathematics Studies, vol.204, Elsevier Science B.V, Amsterdam, 2006.
- Liu, Y., New existence results for positive solutions of boundary value problems for coupled systems of multi-term fractional differential equations, Hacettepe Journal of Mathematics and Statistics, 45(2) (2016), 391-416.
- Xie, S., Xie, Y., Positive solutions of higher order nonlinear fractional differential systems with nonlocal boundary conditions, Journal of Applied Analysis and Computation, 6(4), (2016), 1211-227.
- Podlubny, I., Fractional Differential Equations, Academic Press, San Diego, 1999.
- Su, X., Boundary value problem for a coupled system of nonlinear fractional differential equations, Applied Mathematics Letters, 22 (2009), 64-69.
- Wang, Y., Positive solutions for a system of fractional integral boundary value problem, Boundary Value Problems, (2013), 2013:256.
- Cabrera, I., Harjani, J., Sadarangani, K., Existence and uniqueness of solutions for a boundary value problem of fractional type with nonlocal integral boundary conditions in Holder spaces, Mediterr. J. Math., (2018), 15-98.
- He, J., Zhang, X., Liu, L., Wu, Y., Cui, Y., Existence and asymptotic analysis of positive solutions for a singular fractional differential equation with nonlocal boundary conditions, Boundary Value Problems, (2018), 2018:189.
- Wang, Y., Liang, S., Wang, Q., Existence results for fractional differential equations with integral and multi-point boundary conditions, Boundary Value Problems, (2018), 2018:4.
- Avery, R.I., Peterson, A.C., Three positive fixed points of nonlinear operators on ordered Banach spaces, Comput. Math. Appl. 42 (2001), 313-322.
- Shah, K., Khan, R. A., Multiple positive solutions to a coupled systems of nonlinear fractional differential equations, Springer Plus, (2016), 5:1116.
- Li, C.F., Luo, X.N., Zuhou, Y., Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations, Computers and Mathematics with Applications 59 (2010), 1363-1375.
- Jiang, J., Wang, H., Existence and uniqueness of solutions for a fractioanl differential equation with multi-point boundary value problems, Journal of Applied Analysis and Computation, 9(6) (2019), 2156-2168.
- Ali, A., Samet, B., Shah, K., Khan, R.A., Existence and stability of solution to a toppled systems of differential equations of non-integer order, Boundary Value Problems, (2017), 2017:16.
- Shah, K., Nonlocal boundary value problems for nonlinear toppled system of fractional differential equations, Hacettepe Journal of Mathematics and Statistics, 49 (1) (2020).
- Shah, K., Khan, R.A., Iterative scheme for a coupled system of fractional-order differential equations with three-point boundary conditions, Mathematical Methods in the Applied Sciences, 41(3) (2018), 1047-1053.
- Shah, K., Zeb, S., Khan, R.A., Multiplicity results of multi-point boundary value problem of nonlinear fractional differential equations, Appl. Math. Inf. Sci., 12(3) (2018), 1-8.