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Integral inequalities are considered to be important as they have many applications described by a number of researchers. Moreover, the theory of fractional calculus is used in solving differential, integral, and integro-differential equations and also in various other problems involving special functions. In this research article, we present the improved version of generalizations for a Grüss type integral inequality by taking a generalized Riemann-Liouville fractional integral in terms of a new parameter . We contribute in the on going research by providing mathematical results that can be verified easily.