Solvability of Some Nonlocal Fractional Boundary Value Problems at Resonance in ℝ^<i>n</i>

Abstract

In this paper, the solvability of a system of nonlinear Caputo fractional differential equations at resonance is considered. The interesting point is that the state variable x∈Rn and the effect of the coefficient matrices matrices B and C of boundary value conditions on the solvability of the problem are systematically discussed. By using Mawhin coincidence degree theory, some sufficient conditions for the solvability of the problem are obtained.

Keywords

• coincidence degree theory
• four-point boundary value problem system
• at resonance