Analysis of a fractional eigenvalue problem involving Atangana-Baleanu fractional derivative: A maximum principle and applications.

In this paper, we study linear and nonlinear fractional eigenvalue problems involving the Atangana-Baleanu fractional derivative of the order 1<δ<2. We first estimate the fractional derivative of a function at its extreme points and apply it to obtain a maximum principle for the linear fractional boundary value problem. We then estimate the eigenvalues of the nonlinear eigenvalue problem and obtain necessary conditions to guarantee the existence of eigenfunctions.