Serap Özcan

In this paper, the stochastic-fractional Chen-Lee-Liu equation is analyzed with respect to optical fibres using conformable derivatives. An extensive bifurcation analysis is carried out to understand the many states and transitions of the system. The sensitivity analysis question examines the effect of changes in other parameters on the behaviour of the system itself. The paper presents a novel solution to the complex stochastic-fractional Chen-Lee-Liu equation by applying the improved modified Sardar sub-equation method. The results show that both the modelling and analysis of optical fibre systems affected by stochastic-fractional dynamics made significant progress. Applications of the system are explored in the fields of optical communication and signal processing. Furthermore, the paper includes detailed two-dimensional (2D) and three-dimensional (3D) graphs to illustrate the results visually and authenticate the theoretical results.

A novel category of convex functions, termed multiplicatively trigonometric convex functions, are introduced in this paper. We explore their algebraic characteristics and establish connections between such functions and other forms of convex functions. We even show that these functions are symmetric with respect to their components. Furthermore, we prove the Hermite–Hadamard inequality for the mentioned category of functions. In addition, we present new structures of the Hermite–Hadamard inequality within the framework of multiplicative integrals. By broadening these inequalities, the purpose is to reveal some properties and relations that help the advancement of more robust mathematical techniques.

This manuscript includes the investigation of the idea of a multiplicative harmonic P ‐function and construction of the Hermite–Hadamard inequality for such a sort of functions. We also establish several Hermite–Hadamard type inequalities in the setting of multiplicative calculus. Furthermore, we establish upper bounds for such a particular set of functions. Our conclusions are validated by presenting suitable examples with graphs. Through the analysis of this specific class of convex functions, our aim is to reveal novel mathematical viewpoints, characteristics, and relationships that can improve the advancement of more robust mathematical methodologies. Findings from this study contributes to the development of mathematical tools across a wide range of scientific disciplines.

In this study, we aim to introduce some new definitions called ρ ‐interpolative Ćirić–Reich–Rus‐type and Kannan‐type fuzzy contractions by using the concepts of ρ ‐admissibility (by Dinarvand (2017)) and ς ‐comparison function (by Mihet (2008)). We prove some fixed‐point theorems for ρ ‐interpolative Ćirić–Reich–Rus‐type and Kannan‐type fuzzy contractions in M‐complete fuzzy metric spaces. We presented some of the results established in fuzzy metric spaces to the partially ordered fuzzy metric spaces. Some examples support the results obtained in this manuscript. As an application, we present the existence of a solution to the entity uniqueness problems.

In this study, we prove the existence of a fixed point for a Suzuki‐type δ ‐contraction, which is a generalization of the δ ‐contraction and weak δ ‐contraction mappings. We prove a fixed point theorem for multivalued mappings satisfying a Suzuki‐type δ ‐contraction in complete fuzzy metric spaces. Furthermore, we prove some several fixed point results for single and multivalued mappings in complete fuzzy metric spaces. We establish some examples that support some of the results in our study. As an application, we present the existence and uniqueness of solution for the system of functional equations in dynamic programming.