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Positive Solutions for Nabla Fractional Three-Point Boundary Value Problems

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 the present work is to study a class of nabla fractional problems with two different nabla Riemann–Liouville operators and three-point parameter-dependent boundary conditions. First, we derive the expression of the Green’s function; then, we deduce a few useful inequalities with it, and we establish an interval for the parameter in which the Green’s function is always positive. Using these properties, we manage to prove some non-existence, existence and multiplicity results using different fixed-point theorems. At the end, we give a few examples that verify and clarify the applications of our results.

Suggested Citation

  • Nikolay D. Dimitrov & Jagan Mohan Jonnalagadda, 2026. "Positive Solutions for Nabla Fractional Three-Point Boundary Value Problems," Mathematics, MDPI, vol. 14(6), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:14:y:2026:i:6:p:1086-:d:1901577
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