The existence result of a fuzzy implicit integro-differential equation in semilinear Banach space

Abstract

In this paper‎, ‎the existence and uniqueness of the ‎solution of a nonlinear fully fuzzy implicit integro-differential equation‎<br /> ‎arising in the field of fluid mechanics is investigated. ‎First,‎ an equivalency lemma ‎is ‎presented ‎by‎ which the problem understudy ‎is ‎converted‎ to ‎the‎ two different forms of integral equation depending on the kind of differentiability of the solution. Then, the conditions required to guarantee the existence of a solution for the equivalent integral equation are‎ investigated using the Schauder fixed point theorem in semilinear Banach space.