Existence results for some fractional order coupled systems with impulses and nonlocal conditions on the half line

Abstract. In this paper, we deal with initial value problems for coupled systems of nonlinear fractional differential equations, subject to coupled nonlocal initial and impulsive conditions on the half line. Global existence-uniqueness results are obtained under weak conditions allowing the reaction part of the problem to increase indefinitely with time. Our approach relies mainly to some fixed point theorem of Perov’s type in generalized gauge spaces. The obtained results improve, generalize and complement many existing results in the literature. An example illustrating our main finding is also given. Mathematics Subject Classification (2010): 26A33, 93C23, 35E15, 47H10. Keywords: Fractional differential equation, coupled systems, generalized spaces in Perov’s sens, nonlocal initial conditions, impulses.