Fuzzy Dynamic Equations on Time Scales under Generalized Delta Derivative via Contractive-like Mapping Principles

Abstract

Background/Objectives: The first order nonlinear Fuzzy Dynamic Equations (FDEs) play an important role in recent years to model the dynamic systems with uncertainties and vagueness. The present work deals with obtaining the existence and uniqueness criteria for nonlinear FDEs on time scales which provides a foundation for the nonlinear studies in the field of FDEs. Methods/Statistical Analysis: In place of Banach contraction principle, contractive-like mapping principles on partial ordered sets is used as a tool to study the FDEs on time scales under generalized delta derivative. Findings: The nonlinear FDEs on time scales using generalized delta derivative are not studied so far. The generalized delta derivative is based on four forms which allow us to obtain new solutions for FDEs with decreasing length of their support. Moreover, the differentiability in third and fourth forms is linked with the concept of switching points. These results include both continuous and discrete FDEs under one framework. Application/Improvements: These results are useful to study qualitative and quantitative properties for nonlinear FDEs on time scales which arise in biological, economical and control engineering problems.