On Existence of Multiplicity of Weak Solutions for a New Class of Nonlinear Fractional Boundary Value Systems via Variational Approach

Abstract

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 ℝ 3 and ℝ 4 are given to illustrate the theoritical results.

Certain fractional formulas of the extended k-hypergeometric functions

“…This approach allows the related research work to be reported in further articles. Additionally, all the outcomes presented here are expected to find some applications in control theory and to the solutions of fractional-order systems, for instance, see [43][44][45][46][47] and the references cited therein.…”