Ordered partial modular metric spaces: stability, coincidence point, and fixed point results with application to nonlinear Volterra integro-differential equation

Abstract

In this article, we introduce the notion of ordered partial modular metric spaces and derive novel coincidence point and fixed point results for generalized \((\varphi, \psi)\)-weak contractive type mappings, incorporating both with and without continuity assumptions on the involved mappings. To demonstrate the applicability of our theoretical result, we provide illustrative examples. As an application, we analyze the existence and uniqueness of solutions to nonlinear Volterra integro-differential equation, supported by numerical simulation. Moreover, we establish Hyers-Ulam-Rassias stability for the nonlinear Volterra integro-differential equation by employing the fixed point technique and a numerical example is illustrated to verify the result.