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Some New Application of Extended Wright Function

Author

Listed:
  • Pallavi Sharma
  • Ekta Mittal
  • D. L. Suthar
  • Rajni Gupta

Abstract

This study introduces a novel extension of the Wright function using the Macdonald function as an extension of the Pochhammer symbol. We establish integral, differential, and generating function formulas for this new function. Furthermore, we apply it to fractional differential equations, providing integral transformations of Cauchy‐type problems with graphical representation. The Mellin and Rishi transformations are also derived for the extended Wright function. These results offer new insights and potential applications in fractional calculus (FC), mathematical physics, and engineering. MSC2020 Classification: 26A33, 33B15, 33C05, 65D20, 33E20, 91B25

Suggested Citation

  • Pallavi Sharma & Ekta Mittal & D. L. Suthar & Rajni Gupta, 2025. "Some New Application of Extended Wright Function," Abstract and Applied Analysis, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jnlaaa:v:2025:y:2025:i:1:n:1812741
    DOI: 10.1155/aaa/1812741
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    References listed on IDEAS

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    1. D. L. Suthar & Martin Bohner, 2020. "Composition Formulae for the k-Fractional Calculus Operators Associated with k-Wright Function," Journal of Mathematics, Hindawi, vol. 2020, pages 1-9, July.
    2. Serkan Araci & Gauhar Rahman & Abdul Ghaffar & Azeema & Kottakkaran Sooppy Nisar, 2019. "Fractional Calculus of Extended Mittag-Leffler Function and Its Applications to Statistical Distribution," Mathematics, MDPI, vol. 7(3), pages 1-14, March.
    3. Yuriy Povstenko, 2021. "Some Applications of the Wright Function in Continuum Physics: A Survey," Mathematics, MDPI, vol. 9(2), pages 1-14, January.
    4. Francesco Mainardi & Armando Consiglio, 2020. "The Wright Functions of the Second Kind in Mathematical Physics," Mathematics, MDPI, vol. 8(6), pages 1-26, June.
    5. Yashoverdhan Vyas & Anand V. Bhatnagar & Kalpana Fatawat & D. L. Suthar & S. D. Purohit, 2022. "Discrete Analogues of the Erdélyi Type Integrals for Hypergeometric Functions," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    6. Moustafa El-Shahed & Ahmed Salem, 2015. "An Extension of Wright Function and Its Properties," Journal of Mathematics, Hindawi, vol. 2015, pages 1-11, December.
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