IJPAMR International Journal of Pure and Applied Mathematics Research 2789-9160 SvedbergOpen ijpamr-1-1-002 10.51483/IJPAMR.1.1.2021.21-33 Research Paper Some Theorems in Existence, Uniqueness and Stability Solutions of Volterra Integro-Differential Equations of the First Order ButrisRaad N. 1 * AbdiSahla B. 2 1University of Duhok, College of Basic Education, Department of Mathematics, Iraq. E-mail: raad.butris@uod.ac 2University of Duhok, College of Basic Education, Department of Mathematics, Iraq. E-mail: sahlabebo1@gmail.com *Corresponding author: Raad N. Butris, University of Duhok, College of Basic Education, Department of Mathematics, Iraq. E-mail: raad.butris@uod.ac 10 2021 1 1 21 33 Abstract

We study the existence, uniqueness and stability solutions of new Volterra integrodifferential equations of the first order by using Picard approximation method, Banach fixed point theorem. Theorems on the existence, uniqueness and stability solutions are established under some necessary and sufficient conditions on closed and bounded domains. Furthermore the study of such nonlinear of Volterra integro-differential equations leads us to improve and extend the above methods and thus the non-linear Volterra integrodifferential equations that we have introduced in this study become more general and 3 detailed than those introduced some results by Butris and Rafeq (2011).

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