Existence Results of Fractional Mixed Type Integro-differential Systems through Conformable Fractional Derivatives with Non-instantaneous Impulses

This paper establishes the existence and uniqueness of mild solutions for a novel class of semi-linear fractional integro-differential equations (SFIDEs) of mixed type in a general Banach space E, incorporating non-instantaneous impulses (NIIs) via the conformable fractional derivative (CFD) of order ∈(0,1]. The system features a Volterra-type operator U and a Fredholm-type operator V, both embedded in the nonlinear term, capturing hereditary and global spatial effects respectively. Existence and uniqueness are established via the generalized Banach contraction mapping principle, without imposing additional smallness constraints on the contraction constant, while existence alone is obtained through Krasnoselskii's fixed point theorem under a sub-linear growth condition, within a compact C_0-semigroup framework. An illustrative example on L^2([0,1],R) is provided to validate the theoretical findings.