Abstract
In this paper, we deal with the Caputo–Fabrizio fractional integral operator with a nonsingular kernel and establish some new integral inequalities for the Chebyshev functional in the case of synchronous function by employing the fractional integral. Moreover, several fractional integral inequalities for extended Chebyshev functional by considering the Caputo–Fabrizio fractional integral operator are discussed. In addition, we obtain fractional integral inequalities for three positive functions involving the same operator.
Highlights
Fractional calculus is a generalization of traditional calculus which deals with nonnegative integer order integration and differentials which have various applications in different fields of science and technology
We studied the novel fractional integral inequalities for the Chebyshev and extended the Chebyshev functionals by considering the Caputo–Fabrizio fractional integral operator
We studied some inequalities for three positive functions using the same operator
Summary
Fractional calculus is a generalization of traditional calculus which deals with nonnegative integer order integration and differentials which have various applications in different fields of science and technology. Certain phenomena related to material heterogeneities cannot be well-modeled by considering the Riemann–Liouville and Caputo fractional derivatives due to the singular kernel It stems from Caputo and Fabrizio’s proposal of a new fractional integral involving the nonsingular kernel e−(. In [10,14,16,17,18], the authors have established some new integral inequalities for the Chebyshev and extended Chebyshev functionals using different fractional operators.
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