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We study the existence and multiplicity of solutions for the following fractional boundary value problem: (𝑑/𝑑𝑡)((1/2)0𝐷𝑡−𝛽(𝑢′(𝑡))+(1/2)𝑡𝐷𝑇−𝛽(𝑢′(𝑡)))+∇𝐹(𝑡,𝑢(𝑡))=0,a.e.𝑡∈[0,𝑇],𝑢(0)=𝑢(𝑇)=0, where 𝐹(𝑡,⋅) are superquadratic, asymptotically quadratic, and subquadratic, respectively. Several examples are presented to illustrate our results.