New qualitative results to delay integro-differential equations

Document Type : Research Paper


Department of Computer Programing, Baskale Vocational School, Van Yuzuncu Yil University, 65080, Campus-Van, Van, Turkey


This work deals with various qualitative analyses of solutions of a certain delay integro-differential equation (DIDE). We prove here six new theorems including sufficient conditions, on uniformly stability (US), boundedness, asymptotically stability (AS), exponentially stability (ES), integrability and instability of solutions, respectively.  By defining a suitable Lyapunov function (LF) and using the Razumikhin method (RM), the proofs of the theorems are provided. We gave two examples to demonstrate applications of the established new conditions.


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Volume 13, Issue 2
July 2022
Pages 1131-1141
  • Receive Date: 30 October 2021
  • Revise Date: 02 January 2022
  • Accept Date: 04 February 2022