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

Nikolay D. Dimitrov () and Jagan Mohan Jonnalagadda
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Nikolay D. Dimitrov: Department of Mathematics, University of Ruse, 7017 Ruse, Bulgaria
Jagan Mohan Jonnalagadda: Department of Mathematics, Birla Institute of Technology and Science Pilani, Hyderabad 500078, Telangana, India

Mathematics, 2025, vol. 13, issue 15, 1-14

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.

Keywords: nabla fractional difference equations; fixed-point theorems; uniqueness results; existence result (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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