On Existence of Multiplicity of Weak Solutions for a New Class of Nonlinear Fractional Boundary Value Systems via Variational Approach - Fares Kamache; Salah Mahmoud Boulaaras; Rafik Guefaifia; Nguyen Thanh Chung; Bahri Belkacem Cherif; Mohamed Abdalla (Advances in Mathematical Physics)
This paper deals with the existence of solutions for a new class of nonlinear fractional boundary value systems involving the left and right Riemann-Liouville fractional derivatives. More precisely, we establish the existence of at least three weak solutions for the problem using variational methods combined with the critical point theorem due to Bonano and Marano. In addition, some examples in ℝ3 and ℝ4 are given to illustrate the theoritical results.