Existence and Uniqueness of Solutions to Fractional Differential Equations in Complex-Valued Suprametric Spaces

This study focuses on establishing the existence and uniqueness of solutions for nonlinear fractional differential equations through the application of fixed-point methods in complex-valued suprametric spaces. In order to accomplish this, novel cyclic and interpolative contractive conditions are formulated within the complex-valued suprametric setting, leading to the derivation of several common fixed-point theorems. The obtained results extend and encompass a variety of known fixed-point theorems in complex-valued metric spaces as particular instances. In addition, meaningful and non-trivial examples are presented to highlight the effectiveness and practical relevance of the developed theoretical framework.