On different generalized interpolative proximal-type contractions in metric spaces with applications

In this work, we establish the conditions for ensuring the existence and uniqueness of common best proximity points for non-self-mappings defined on the general metric spaces. A unified theoretical framework is formulated to cover a broad class of contraction mappings. We describe the required conditions on the real-valued functions (ℵ, Φ) : [0,∞) → R and verify that these secure the existence of common best proximity points for (ℵ, Φ)−interpolative contractions in complete metric spaces. The study further extends this concept by examining multiple forms of interpolative proximal-type contractions, such as proximal, Ćirić —Reich—Rus, Kannan, and Hardy-Rogers variants, through the use of the auxiliary functions (ℵ, Φ). Several illustrated examples are included to demonstrate the applicability of our findings. Finally, we conclude with an application involving a nonlinear fractional differential equation, showing that it fully satisfies the assumption of our main result.