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In the paper we prove several inequalities involving two isotonic linearfunctionals. We consider inequalities for functions with variable bounds, forLipschitz and H\" older type functions etc. These results give us an elegantmethod for obtaining a number of inequalities for various kinds of fractionalintegral operators such as for the Riemann-Liouville fractional integraloperator, the Hadamard fractional integral operator, fractional hyperqeometricintegral and corresponding q-integrals.

Unified treatment of fractional integral inequalities via linear functionals