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Some Incomplete Hypergeometric Functions and Incomplete Riemann-Liouville Fractional Integral Operators

Author

Listed:
  • Mehmet Ali Özarslan

    (Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University, Famagusta, TRNC, Mersin 10, Turkey)

  • Ceren Ustaoğlu

    (Department of Computer Engineering, Final International University, Toroslar Caddesi, No. 6, Çatalköy, Girne, TRNC, Mersin 10, Turkey)

Abstract

Very recently, the incomplete Pochhammer ratios were defined in terms of the incomplete beta function B y ( x , z ) . With the help of these incomplete Pochhammer ratios, we introduce new incomplete Gauss, confluent hypergeometric, and Appell’s functions and investigate several properties of them such as integral representations, derivative formulas, transformation formulas, and recurrence relations. Furthermore, incomplete Riemann-Liouville fractional integral operators are introduced. This definition helps us to obtain linear and bilinear generating relations for the new incomplete Gauss hypergeometric functions.

Suggested Citation

  • Mehmet Ali Özarslan & Ceren Ustaoğlu, 2019. "Some Incomplete Hypergeometric Functions and Incomplete Riemann-Liouville Fractional Integral Operators," Mathematics, MDPI, vol. 7(5), pages 1-18, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:483-:d:234755
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