## Boundary value problem for a coupled system of nonlinear fractional differential equations.(English)Zbl 1163.34321

Summary: In this work we discuss a boundary value problem for a coupled differential system of fractional order. The differential operator is taken in the Riemann-Liouville sense and the nonlinear term depends on the fractional derivative of an unknown function. By means of Schauder fixed-point theorem, an existence result for the solution is obtained. Our analysis relies on the reduction of the problem considered to the equivalent system of Fredholm integral equations.

### MSC:

 34B15 Nonlinear boundary value problems for ordinary differential equations 26A33 Fractional derivatives and integrals
Full Text:

### References:

 [1] Podlubny, I., () [2] Kilbas, A.A.; Srivastava, H.M.; Trujillo, J.J., Theory and applications of fractional differential equations, (2006), Elsevier B.V. Amsterdam · Zbl 1092.45003 [3] Nakhushev, A.M., The sturm – liouville problem for a second order ordinary differential equation with fractional derivatives in the lower terms, Dokl. akad. nauk SSSR, 234, 308-311, (1977) · Zbl 0376.34015 [4] Aleroev, T.S., The sturm – liouville problem for a second order ordinary differential equation with fractional derivatives in the lower terms, Differ. uravneniya, 18, 2, 341-342, (1982), (in Russian) · Zbl 0487.34019 [5] Zhang, S.Q., Existence of solution for a boundary value problem of fractional order, Acta math. sci., 26B, 2, 220-228, (2006) · Zbl 1106.34010 [6] Zhang, S.Q., Positive solutions for boundary-value problems of nonlinear fractional differential equations, Electron. J. differential equations, 36, 1-12, (2006) [7] Bai, Z.B.; Lü, H.S., Positive solutions for boundary value problem of nonlinear fractional differential equation, J. math. anal. appl., 311, 2, 495-505, (2005) · Zbl 1079.34048 [8] Bai, C.Z.; Fang, J.X., The existence of a positive solution for a singular coupled system of a nonlinear fractional differential equations, Appl. math. comput., 150, 3, 611-621, (2004) · Zbl 1061.34001 [9] Y. Chen, H-L. An, Numerical solutions of coupled Burgers equations with time- and space-fractional derivatives, Appl. Math. Comput. (in press) [10] V. Gafiychuk, B. Datsko, V. Meleshko, Mathematical modeling of time fractional reaction – diffusion systems, J. Comput. Appl. Math. (in press) · Zbl 1152.45008 [11] Deng, W.H.; Li, C.P., Chaos synchronization of the fractional Lü system, Physica A, 353, 61-72, (2005)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.