Eigenvalue problems for fractional differential equations with mixed derivatives and generalized p-Laplacian

This paper reports the investigation of eigenvalue problems for two classes of nonlinear fractional differential equations with generalized p-Laplacian operator involving both Riemann-Liouville fractional derivatives and Caputo fractional derivatives. By means of fixed point theorem on cones, some sufficient conditions are derived for the existence, multiplicity and nonexistence of positive solutions to the boundary value problems. Finally, an example is presented to further verify the correctness of the main theoretical results and illustrate the wide range of their potential applications.