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On Saigo-type Fractional Integrals of Generalized Q-Functions and Their Applications to Extended Mittag–Leffler and Wright Functions

Author

Listed:
  • Priyanka Vaijanathrao Sanap
  • Tarachand L. Holambe
  • Bhausaheb R. Sontakke

Abstract

This paper presents a comprehensive study of the Saigo-type fractional integral operator S0 α + ,β,γ applied to a broad class of generalized Q-functions Qσ κ, , ζ ξ , , η v, , r ϑ,τ ,ρ(t) characterized by multiple complex parameters. We establish explicit closed-form expressions for fractional integrals of weighted generalized Q-functions in terms of Hadamard products involving the original functions and Wright-type hypergeometric functions 2Ψ1. Detailed numerical examples with explicit parameter values demonstrate the computational feasibility and practical applicability of the derived formulas. The results contribute significantly to fractional calculus theory and provide valuable tools for solving fractional differential equations involving generalized special functions with memory effects.

Suggested Citation

  • Priyanka Vaijanathrao Sanap & Tarachand L. Holambe & Bhausaheb R. Sontakke, 2025. "On Saigo-type Fractional Integrals of Generalized Q-Functions and Their Applications to Extended Mittag–Leffler and Wright Functions," European Journal of Mathematics and Statistics, European Open Science, vol. 6(6), pages 13-23, November.
    • Handle: RePEc:epw:ejmath:v:6:y:2025:i:6:id:14420
    DOI: 10.24018/ejmath.2025.6.6.420
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