Eigenvalue and Nonlinear Fractional Problems with Riemann Liouville Operator

Abstract

This thesis investigates nonlinear fractional differential equations involving Riemann–Liouville derivatives. After introducing the appropriate functional framework, we study two nonlinear fractional problems within a variational setting. The first problem, which is a nonlinear eigenvalue problem, is studied using the minimization method to establish the existence of weak solutions. The second problem is a general nonlinear fractional equation, where two cases are considered: the sublinear case, treated via a minimization method, and the superlinear case, analyzed using the Nehari manifold technique.