Global Existence and Uniqueness of Solutions of Integral Equations with Multiple Variable Delays and Integro Differential Equations: Progressive Contractions
Osman Tunç, Cemil Tunç, Jen‐Chih Yao
Abstract
In this work, we delve into a nonlinear integral equation (IEq) with multiple variable time delays and a nonlinear integro-differential equation (IDEq) without delay. Global existence and uniqueness (GEU) of solutions of that IEq with multiple variable time delays and IDEq are investigated by the fixed point method using progressive contractions, which are due to T.A. Burton. We prove four new theorems including sufficient conditions with regard to GEU of solutions of the equations. The results generalize and improve some related published results of the relevant literature.
Topics & Concepts
UniquenessMathematicsNonlinear systemVariable (mathematics)Differential equationFixed-point theoremIntegro-differential equationApplied mathematicsMathematical analysisIntegral equationWork (physics)First-order partial differential equationPhysicsQuantum mechanicsThermodynamicsFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisNumerical methods for differential equations