# A Note on \(K_4\) Fractional Integral Operator

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## Abstract

The present paper deals with the study of new generalized fractional integral operator involving \(K_4\)-function due to Sharma. Mellin and Laplace transforms of this new operator are investigated. The bounded-ness and composition properties of the proposed operator are also established. Further, derived results are applied to solve fractional differential equation involving \(K_4\)-function associated with Hilfer derivatives. The \(K_4\)-function is further extension of *M*-series and the importance of desired results lies in the fact that many known results are readily follows as special cases of our finding. \(K_4\) and *M*-series have recently found essential application in solving problems of science, engineering and technology. Some special cases of the established results are given in form of corollaries.

## Keywords

\(K_4\)-function*M*-series Fractional integral operator

*H*-function Generalized Wright function

## Mathematics Subject Classification

Primary 44A10 26A33 Secondary 33C20 33C05 33E12## Notes

### Acknowledgements

The author (Dinesh Kumar) would like to express his deep thanks to NBHM (National Board of Higher Mathematics), India, for granting a Post-Doctoral Fellowship (Sanction No. 2/40(37)/2014/R&D-II/14131).

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