About reducing integro-differential equations with infinite limits of integration to systems of ordinary differential equations

*Correspondence: [email protected] Department of Mathematics and Computer Sciences, Ariel University of Samaria, Ariel, Israel Abstract The purpose of this paper is to propose a method for studying integro-differential equations with infinite limits of integration. The main idea of this method is to reduce integro-differential equations to auxiliary systems of ordinary differential equations. Results: a scheme of the reduction of integro-differential equations with infinite limits of integration to these auxiliary systems is described and a formula for representation of bounded solutions, based on fundamental matrices of these systems, is obtained. Conclusion:methods proposed in this paper could be a basis for the Floquet theory and studies of stability, bifurcations, parametric resonance and various boundary value problems. As examples, models of tumor-immune system interaction, hematopoiesis and plankton-nutrient interaction are considered. MSC: 45J05; 45J15; 34A12; 34K05; 34K30; 47G20