By employing the Saigo k-fractional integral operators, some new inequalities for the Chebyshev functional are formulated for two synchronous functions in this article. Further generalisations of these inequalities, including three monotonous functions, are also mentioned. In addition, as special cases of our key results, inequalities for the Chebyshev functional about Saigo fractional integrals are obtained. The main results are of a general nature and, as a special case, give rise to integral inequalities describing the Saigo's, Riemann-Liouville and Erdélyi-Kober fractional integral operators referred to the literature.
In this paper, we investigate the fractional derivatives and expansion formulae of incomplete $H$ and $\overline{H}$-functions for one variable. Further, we also obtain results for repeated fractional order derivatives and some special cases are also discussed. Various other analogues results are also established. The results obtained here are very much helpful for the further research and useful in the study of applied problems of sciences, engineering and technology.
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