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Existence and Non-existence of Positive Solutions for a Discrete Fractional Boundary Value Problem |
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| Authors: | Jagan Mohan Jonnalagadd N. S. Gopal |
| Affiliation: | Department of Mathematics, Birla Institute of Technology and Science Pilani, Hyderabad-500078, Telangana, India; Department of Mathematics, Birla Institute of Technology and Science Pilani, Hyderabad-500078, Telangana, India; Presidency College, Hebbal, Bangalore-560058, Karnataka, India |
| 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. |
| Keywords: | Nabla fractional difference dirichlet boundary conditions boundary value problem Green''s function fixed-point positive solution eigenvalue |
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