EIGENVALUE PROBLEM FOR A NABLA FRACTIONAL DIFFERENCE EQUATION WITH DUAL NONLOCAL BOUNDARY CONDITIONS

N. S. Gopal; Jagan Mohan Jonnalagadda

doi:10.11948/20210506

2023 Volume 13 Issue 2

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N. S. Gopal, Jagan Mohan Jonnalagadda. EIGENVALUE PROBLEM FOR A NABLA FRACTIONAL DIFFERENCE EQUATION WITH DUAL NONLOCAL BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2023, 13(2): 684-700. doi: 10.11948/20210506

Citation:

N. S. Gopal, Jagan Mohan Jonnalagadda. EIGENVALUE PROBLEM FOR A NABLA FRACTIONAL DIFFERENCE EQUATION WITH DUAL NONLOCAL BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2023, 13(2): 684-700. doi: 10.11948/20210506

EIGENVALUE PROBLEM FOR A NABLA FRACTIONAL DIFFERENCE EQUATION WITH DUAL NONLOCAL BOUNDARY CONDITIONS

N. S. Gopal¹,
Jagan Mohan Jonnalagadda^1, ,

1.
Department of Mathematics, Birla Institute of Technology and Science Pilani, Hyderabad - 500078, Telangana, India

Corresponding author: Email: j.jaganmohan@hotmail.com(J. M. Jonnalagadda)

Abstract

Abstract

In this work, we study the existence of positive solutions for the non-local boundary value problem for a finite nabla fractional difference equation with a parameter $ \beta>0 $
$ \begin{equation*} \label{BVP N} \begin{cases} -\big{(}\nabla^{\alpha}_{\rho(a)} u\big{)}(t) = \beta f(t, u(t)), \quad t \in \mathbb{N}^{b}_{a + 2}, \\ u(a) = g_1(u),\quad u(b) = g_2(u). \end{cases} \end{equation*} $
With the help of properties of the Green's functions and appropriate conditions on the non-linear part of the difference equation, we are able to construct the eigenvalue intervals of the considered boundary value problem using Guo–Krasnoselskii fixed point theorem on a suitable cone. Finally, we provide a couple of examples to demonstrate the applicability of established results.
- Nabla fractional difference /
- eigenvalue problem /
- parameter /
- fixed point /
- positive solution
MSC: 39A12

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References

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