New α-ɛ-Suzuki-Type Contraction Mapping Methods on Fractional Differential and Integral Equations

This paper introduces novel formulations in the framework of α−E-contractions within the context of admissible mappings. We establish new fixed point theorems for α−E-Suzuki-type contractions, thereby generalizing and extending the foundational work of Hossein Piri and Poom Kumam. The principal objective of this research is to investigate the existence and uniqueness of solutions to a class of integral equations by leveraging fixed point methodologies in complete metric spaces. By developing these advanced α−E-contraction concepts and analyzing their implications for admissible mappings, this work contributes to the theoretical advancement of fixed point theory. To support our new definition, we illustrate examples. The results demonstrate the efficacy of this approach for addressing nonlinear problems in analysis, specifically enriching the methodology for solving integral equations. The overarching aim is to consolidate the theoretical underpinnings and provide a rigorous analytical framework for the application of α−E-contraction mappings, thereby fostering further progress in mathematical analysis.