Multiple Positive Solutions of Discrete Fractional Boundary Value Problems
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Authors: N. S. GOPAL AND J. M. JONNALAGADDA
DOI: 10.46793/KgJMat2601.025G
Abstract:
In this work, we deal with the following two-point non-linear Dirichlet boundary value problem for a finite nabla fractional difference equation:
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Here a, b ∈ ℝ with b−a ∈ ℕ3, 1 < α < 2, f : ℝ → ℝ+ ∪{0} is a continuous function, and ∇ρ(a)α denotes the αth order Riemann-Liouville nabla difference operator. First, we construct an associated Green’s function and obtain some of its properties. Under suitable conditions on the non-linear part of the difference equation, we deduce some results for at least two and at least three positive solutions of the considered problem. For this purpose, we use a few prominent conical shell fixed point theorems.
Keywords:
Nabla fractional difference, boundary value problem, Dirichlet boundary conditions, Green’s function, cone, fixed point, positive solution.
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