Solving integro-differential equation in orthogonal partial b-metric spaces via simulation function

Abstract

In our research, we delve into exploring the presence and singular nature of a stable point amidst nearly orthogonal almost Z-contractions, facilitated by simulation functions within fully developed orthogonal partial b-metric spaces, employing orthogonal (ˆ∝, ˆβ)-admissibility. Additionally, we provide demonstrative instances to substantiate the outcomes. Moreover, we offer an application to integro-differential equations, thereby contributing to the expansion and enhancement of various prior studies in the field.