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Received January 19, 2017; Accepted May 10, 2017; Published May 22, 2017
Abstract. Some results regarding the existence of solutions for a nonlinear higher order fractional differential equation involving both the left Riemann-Liouville and the right Caputo fractional derivatives with a natural boundary condition are obtained. The results presented in this paper are based on the method of upper and lower solutions and the monotonicity of the right Caputo derivative. Moreover, we give the explicit expression of the lower and upper solutions. Two illustrative numerical examples are also provided.
How to Cite this Article:
Rabah Khaldi, Assia Guezane-Lakoud, Higher order fractional boundary value problems for mixed type derivatives, Journal of Nonlinear Functional Analysis, Vol. 2017 (2017), Article ID 30, pp. 1-9.