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In this paper, we prove several inequalities of the Grüss type involving generalized k -fractional Hilfer–Katugampola derivative. In 1935, Grüss demonstrated a fascinating integral inequality, which gives approximation for the product of two functions. For these functions, we develop some new fractional integral inequalities. Our results with this new derivative operator are capable of evaluating several mathematical problems relevant to practical applications.

Some k-fractional extension of Grüss-type inequalities via generalized Hilfer–Katugampola derivative