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Article

Existence and Uniqueness of Solutions to a Nabla Fractional Difference Equation with Dual Nonlocal Boundary Conditions

Department of Mathematics, Birla Institute of Technology and Science Pilani, Hyderabad 500078, India
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Academic Editor: Sotiris K. Ntouyas
Foundations 2022, 2(1), 151-166; https://doi.org/10.3390/foundations2010009
Received: 30 December 2021 / Revised: 17 January 2022 / Accepted: 17 January 2022 / Published: 21 January 2022
(This article belongs to the Special Issue Recent Advances in Fractional Differential Equations and Inclusions)
In this paper, we look at the two-point boundary value problem for a finite nabla fractional difference equation with dual non-local boundary conditions. First, we derive the associated Green’s function and some of its properties. Using the Guo–Krasnoselkii fixed point theorem on a suitable cone and under appropriate conditions on the non-linear part of the difference equation, we establish sufficient requirements for at least one and at least two positive solutions of the boundary value problem. Next, we discuss the existence and uniqueness of solutions to the considered problem. For this purpose, we use Brouwer and Banach fixed point theorem, respectively. Finally, we provide a few examples to illustrate the applicability of established results. View Full-Text
Keywords: nabla fractional difference; boundary value problem; fixed point; positive solution; existence; uniqueness nabla fractional difference; boundary value problem; fixed point; positive solution; existence; uniqueness
MDPI and ACS Style

Gopal, N.S.; Jonnalagadda, J.M. Existence and Uniqueness of Solutions to a Nabla Fractional Difference Equation with Dual Nonlocal Boundary Conditions. Foundations 2022, 2, 151-166. https://doi.org/10.3390/foundations2010009

AMA Style

Gopal NS, Jonnalagadda JM. Existence and Uniqueness of Solutions to a Nabla Fractional Difference Equation with Dual Nonlocal Boundary Conditions. Foundations. 2022; 2(1):151-166. https://doi.org/10.3390/foundations2010009

Chicago/Turabian Style

Gopal, Nandhihalli Srinivas, and Jagan Mohan Jonnalagadda. 2022. "Existence and Uniqueness of Solutions to a Nabla Fractional Difference Equation with Dual Nonlocal Boundary Conditions" Foundations 2, no. 1: 151-166. https://doi.org/10.3390/foundations2010009

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