Global solutions of fuzzy integro-differential equations under generalized differentiability by the method of upper and lower solutions

This paper is devoted to introduce a new concept of upper and lower solutions for fuzzy integro-differential equations, that is defined on integral equations associated with the main problem. This plays an essential role in proof of existence and uniqueness results under weak conditions. By the method of upper and lower solutions, existence and uniqueness of global solutions of an initial value problem for first-order nonlinear fuzzy integro-differential equation under generalized differentiability are given. Our technique is illustrated by some examples.