Existence and uniqueness of solutions for a class of fractional nonlinear boundary value problems under mild assumptions

Abstract

Abstract We deal with the following Riemann–Liouville fractional nonlinear boundary value problem: { D α v ( x ) + f ( x , v ( x ) ) = 0 , 2 0 . $$ \bigl\vert v(x) \bigr\vert \leq cx^{\alpha -1}(1-x)\quad\text{for all }x \in [ 0,1]\text{ and some }c>0. $$ Our results improve those obtained by Zou and He (Appl. Math. Lett. 74:68–73, 2017).

Keywords

• Fractional differential equation
• Green’s function
• Existence and uniqueness of solution
• Banach’s contraction principle