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Some Applications of Analytic Functions Associated with q -Fractional Operator

Author

Listed:
  • Nazar Khan

    (Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22500, Pakistan)

  • Shahid Khan

    (Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22500, Pakistan)

  • Qin Xin

    (Faculty of Science and Technology, University of the Faroe Islands, Vestarabryggja 15, FO 100 Torshavn, Faroe Islands, Denmark)

  • Fairouz Tchier

    (Mathematics Department, College of Science, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia)

  • Sarfraz Nawaz Malik

    (Department of Mathematics, COMSATS University Islamabad, Wah Campus, Wah Cantt 47040, Pakistan)

  • Umer Javed

    (Department of Electrical and Computer Engineering, COMSATS University Islamabad, Wah Campus, Wah Cantt 47040, Pakistan)

Abstract

This paper introduces a new fractional operator by using the concepts of fractional q -calculus and q -Mittag-Leffler functions. With this fractional operator, Janowski functions are generalized and studied regarding their certain geometric characteristics. It also establishes the solution of the complex Briot–Bouquet differential equation by using the newly defined operator.

Suggested Citation

  • Nazar Khan & Shahid Khan & Qin Xin & Fairouz Tchier & Sarfraz Nawaz Malik & Umer Javed, 2023. "Some Applications of Analytic Functions Associated with q -Fractional Operator," Mathematics, MDPI, vol. 11(4), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:930-:d:1065963
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    References listed on IDEAS

    as
    1. Rabha W. Ibrahim, 2012. "Ulam-Hyers Stability for Cauchy Fractional Differential Equation in the Unit Disk," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-10, July.
    2. F. M. Al-Oboudi, 2004. "On univalent functions defined by a generalized Sălăgean operator," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-8, January.
    3. Isra Al-Shbeil & Afis Saliu & Adriana Cătaş & Sarfraz Nawaz Malik & Semiu Oladipupo Oladejo, 2022. "Some Geometrical Results Associated with Secant Hyperbolic Functions," Mathematics, MDPI, vol. 10(15), pages 1-13, July.
    4. Rabha W. Ibrahim, 2012. "Ulam Stability for Fractional Differential Equation in Complex Domain," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-8, January.
    5. Lei Shi & Muhammad Arif & Mohsan Raza & Muhammad Abbas, 2022. "Hankel Determinant Containing Logarithmic Coefficients for Bounded Turning Functions Connected to a Three-Leaf-Shaped Domain," Mathematics, MDPI, vol. 10(16), pages 1-10, August.
    Full references (including those not matched with items on IDEAS)

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