Abstract
In this paper, we establish some new integral inequalities involving general kernels. We obtain the related broad range of fractional integral inequalities. Also, we apply the Young inequality to find new forms of inequalities for generalized kernels. These new and motivated results generalize the results for fractional integrals such that fractional integral of a function with respect to an increasing function, Riemann–Lioville fractional integrals, Erdélyi–Kober fractional integrals, Hadamard fractional integrals, generalized factional integral integrals in addition to the corresponding k-fractional integrals.
Highlights
Fractional calculus deals with the study of derivative and integral operators of fractional order
Our main purpose in this paper is showing some new modifications of the Grüss inequality by using a general kernel
We present the definition of the Erdélyi–Kober-type fractional integrals
Summary
Fractional calculus deals with the study of derivative and integral operators of fractional order. The left- and right-sided fractional integrals of a function f with respect to g in [a, b] are given by The left- and right-sided fractional integrals of a function f with respect to g of order α, k > 0 in [a, b] are given by
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