Fractional differential equations with arbitrary kernel dependence and boundary constraints

In this work, we study fractional differential equations where the fractional derivative depends on an arbitrary function. An additional condition is imposed at an interior point of the problem's domain. First, we reformulate the problem as an integral equation with kernel dependence. We then prove several results regarding the existence and uniqueness of solutions by applying Banach's Fixed Point Theorem, Schaefer's Fixed Point Theorem, and Krasnoselskii's Fixed Point Theorem.