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Existence Results for Nabla Fractional Problems with Anti-Periodic Boundary Conditions

Author

Listed:
  • Nikolay D. Dimitrov

    (Department of Mathematics, University of Ruse, 7017 Ruse, Bulgaria
    These authors contributed equally to this work.)

  • Jagan Mohan Jonnalagadda

    (Department of Mathematics, Birla Institute of Technology and Science Pilani, Hyderabad 500078, Telangana, India
    These authors contributed equally to this work.)

Abstract

The aim of this work is to study a class of nabla fractional difference equations with anti-periodic conditions. First, we construct the related Green’s function. After deducing some of its useful properties, we obtain an upper bound for its sum. Then, using this bound, we are able to obtain three existence results based on the Banach contraction principle, Brouwer’s fixed point theorem, and Leray–Schauder’s nonlinear alternative, respectively. Then, we show some non-existence results for the studied problem, and existence results are also provided for a system of two equations of the considered type. Finally, we outline some particular examples in order to demonstrate the theoretical findings.

Suggested Citation

  • Nikolay D. Dimitrov & Jagan Mohan Jonnalagadda, 2025. "Existence Results for Nabla Fractional Problems with Anti-Periodic Boundary Conditions," Mathematics, MDPI, vol. 13(15), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:15:p:2487-:d:1716126
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