This paper deals with the existence and numerical estimates of solutions for a class of fractional differential equations, while the nonlinear part of the problem admits some Special hypotheses. In particular, for a precise localization of the parameter, the existence of a non-zero solution is established requiring the sublinearity of nonlinear part at origin and infinity. Moreover, theoretical and numerical examples of applications are provided.

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In this paper, we study the existence and the numerical estimates of the solutions for a set of fractional differential equations. The nonlinear part of the problem, however, presupposes certain hypotheses. Particularly, for the exact localization of the parameter, the existence of a non-zero solution is established, which requires the sublinearity of the nonlinear part at origin and infinity. The novelty of this paper is to use variational methods to obtain the multiplicity of solutions of boundary value problems with the nonlinearity depending on the fractional derivative.