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| Existence and Non-existence of Positive Solutions for a Discrete Fractional Boundary Value Problem |
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| KeyWord:Nabla fractional difference, dirichlet boundary conditions, boundary value problem, Green's function, fixed-point, positive solution, eigenvalue |
| Author Name | Affiliation | | Jagan Mohan Jonnalagadda | Department of Mathematics, Birla Institute of Technology and Science Pilani, Hyderabad-500078, Telangana, India | | N. S. Gopal | Department of Mathematics, Birla Institute of Technology and Science Pilani, Hyderabad-500078, Telangana, India
Presidency College, Hebbal, Bangalore-560058, Karnataka, India |
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| Abstract: |
| In this work, we deal with two-point boundary problem for a finite nabla fractional difference equation. First, we establish an associated Green's function and state some of its properties. Under suitable conditions, we deduce the existence and non-existence of positive solutions to the considered problem. Finally, we construct a few examples to illustrate the established results. |
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