Work

Fixed Point Theorems in Complex-Valued b-Suprametric Spaces with Applications to Fractional Differential Equations

Year: 2026

Type: article

Abstract: In this research article, we introduce and develop the notion of complex-valued b-suprametric spaces as a natural generalization of existing metric-type structures. Fundamental concepts, including convergence, Cauchy sequences, and completeness, are examined in this new setting. We establish new common fixed point theorems for generalized and cyclic rational contractive mappings. The obtained results extend and unify various known fixed point theorems available in the current literature. To demonstrate the applicability and effectiveness of our theoretical findings, illustrative nontrivial examples are provided. As an application, we investigate the existence and uniqueness of solutions for Caputo fractional differential equations, which naturally arise in systems with hereditary and memory effects, particularly in biomedical modeling of viscoelastic biological tissues such as arteries, cartilage, and brain tissue. This demonstrates both the mathematical strength and the practical relevance of the proposed framework.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract10040258

Authors: Maha Noorwali, Afrah Ahmad Noman Abdou

Institutions: King Abdulaziz University, University of Jeddah

Language: English

Topic: Fixed Point Theorems Analysis

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,258

Funder: King Abdulaziz University