Advances in Dynamical Systems and Applications (ADSA). ISSN 0973-5321, Volume 16, Number 2, (2021) pp. 457-467 c Research India Publications http://www.ripublication.com/adsa.htm Existence and Uniqueness Results for BVP of Nonlinear Fractional Volterra-Fredholm Integro-Differential Equation Muhammed F. Younis 1 , Ayoob M. Abed 2 , and Ahmed A. Hamoud 3 1,2 Department of Mathematics, Thi Qar Directorates of Education, Ministry of Education, Iraq. 3 Department of Mathematics, Taiz University, Taiz, Yemen. Abstract In this paper, we establish sufficient conditions for the existence and uniqueness of solutions for a class of boundary value problems (BVPs) with nonlocal conditions for nonlinear fractional Volterra-Fredholm integro-differential equations. The results are established by the application of the Arzela-Ascoli theorem, Banach and Krasnoselkii fixed point theorems. Keywords: Volterra-Fredholm integro-differential equations; Caputo fractional derivatives; fixed point method; nonlocal conditions. Mathematics Subject Classification (2010): 26A33, 47H10, 45J05. 1. INTRODUCTION Many applicable models in physical, nonlinear dynamics, biological and chemical sciences can be described successfully using integro-differential equations. For example, the biological population models rely on the delayed Volterra integro-differential equations, systems of integro-differential equations characterize the evolution of nuclear reactor in a continuous medium, and many other problems in viscoelasticity, mechanics and economics as well [1, 8, 17, 19, 20]. Furthermore, converting initial and boundary value problems yields these types of equations [6, 13, 15, 21, 22]. * Corresponding author: muhammedfaleh@yahoo.com;ayob.moha75@gmail. com;ahmed.hamoud@taiz.edu.ye