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Received June 16, 2017; Accepted February 12, 2018; Published February 23, 2018
Abstract. In this paper, based on the upper and lower solutions method and monotone iterative techniques, we study the existence of solutions for fractional differential systems with continuous nonlinearities and integral boundary conditions. The construction of the monotone sequences and the definition of upper and lower solutions depend on the quasimonotone property of the reaction functions. We prove the existence of maximal and minimal solutions for quasimonotone increasing systems. Also, we prove the existence of maximal-minimal and minimal-maximal solutions for quasimonotone decreasing systems and for mixed quasimonotone systems and the existence of at least one solution. Finally, we give some examples to illustrate our results.
How to Cite this Article:
Mohammed Derhab, Fatiha Meziane, Existence results and the monotone iterative techniques for systems of nonlinear fractional differential equations with integral boundary conditions, Journal of Nonlinear Functional Analysis, Vol. 2018 (2018), Article ID 9, pp. 1-22.