The goal of this paper is to present a new space, a complex valued controlled rectangular - metric space (for short, - metric space). Some examples and topological properties of - metric spaces are given. Also, some related common fixed point results are discussed. Our results generalize a lot of works in this direction. Moreover, we apply the theoretical results to find a unique solution of a complex valued Atangana-Baleanu fractional integral operator and a system of complex linear equations. Finally, a numerical example to find the current that passes through the RLC circuit is illustrated.
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