A Note on \(K_4\) Fractional Integral Operator

  • Arif M. Khan
  • Pankaj Ramani
  • Daya Lal Suthar
  • Dinesh Kumar
Original Paper

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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Copyright information

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Authors and Affiliations

  1. 1.Department of MathematicsJodhpur Institute of Engineering and TechnologyJodhpurIndia
  2. 2.Department of MathematicsPoornima UniversityJaipurIndia
  3. 3.Department of MathematicsWollo UniversityWollo DessieEthiopia
  4. 4.Department of Mathematics & StatisticsJai Narain Vyas UniversityJodhpurIndia

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