#### Choukri Derbazi, Hadda Hammouche, Mouffak Benchohra, Weak solutions for some nonlinear fractional differential equations with fractional integral boundary conditions in Banach spaces, Vol. 2019 (2019), Article ID 7, pp. 1-11

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DOI: 10.23952/jnfa.2019.7

Received November 11, 2018; Accepted February 16, 2019; Published February 26, 2019

Abstract. In this paper, we study the existence of weak solutions for some nonlinear fractional differential equations with fractional integral boundary conditions involving the fractional Caputo derivative of order $1 < \alpha \leq 2$ in Banach spaces. Our main results are proved by applying the Mönch’s fixed point theorem combined with the technique of measures of weak noncompactness. In addition, an example is given to demonstrate the applications of our results.