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While it is known that one can consider the existence of solutions to boundary-value problems for fractional differential equations with derivative terms, the situations for the multiplicity of weak solutions for the p-Laplacian fractional differential equations with derivative terms are less considered. In this article, we propose a new class of p-Laplacian fractional differential equations with the Caputo derivatives. The multiplicity of weak solutions is proved by the variational method and critical point theorem. At the end of the article, two examples are given to illustrate the validity and practicality of our main results.

Multiplicity solutions for a class of p-Laplacian fractional differential equations via variational methods