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Existence and Non-existence of Positive Solutions for a Discrete Fractional Boundary Value Problem
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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