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Volume 5, Issue 3
Existence and Non-Existence of Positive Solutions for a Discrete Fractional Boundary Value Problem

N. S. Gopal & Jagan Mohan Jonnalagadda

DOI: 10.12150/jnma.2023.432

J. Nonl. Mod. Anal., 5 (2023), pp. 432-445.

Published online: 2023-08

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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.

  • Keywords

Nabla fractional difference, dirichlet boundary conditions, boundary value problem, Green's function, fixed-point, positive solution, eigenvalue.

  • AMS Subject Headings

39A12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-5-432, author = {Gopal , N. S. and Jonnalagadda , Jagan Mohan}, title = {Existence and Non-Existence of Positive Solutions for a Discrete Fractional Boundary Value Problem}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {5}, number = {3}, pages = {432--445}, 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.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2023.432}, url = {http://global-sci.org/intro/article_detail/jnma/21944.html} }
TY - JOUR T1 - Existence and Non-Existence of Positive Solutions for a Discrete Fractional Boundary Value Problem AU - Gopal , N. S. AU - Jonnalagadda , Jagan Mohan JO - Journal of Nonlinear Modeling and Analysis VL - 3 SP - 432 EP - 445 PY - 2023 DA - 2023/08 SN - 5 DO - http://doi.org/10.12150/jnma.2023.432 UR - https://global-sci.org/intro/article_detail/jnma/21944.html KW - Nabla fractional difference, dirichlet boundary conditions, boundary value problem, Green's function, fixed-point, positive solution, eigenvalue. AB -

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.

N. S. Gopal & Jagan Mohan Jonnalagadda. (2023). Existence and Non-Existence of Positive Solutions for a Discrete Fractional Boundary Value Problem. Journal of Nonlinear Modeling and Analysis. 5 (3). 432-445. doi:10.12150/jnma.2023.432
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