EXISTENCE AND UNIQUENESS OF SOLUTIONS
FOR A DISCRETE FRACTIONAL BOUNDARY
VALUE PROBLEM
A. George Maria Selvam1, R. Dhineshbabu2
1,2Department of Mathematics
Sacred Heart College (Autonomous)
Tirupattur, 635601, Tamil Nadu, INDIA

Abstract

This present work discusses existence and uniqueness of solutions for the following discrete fractional antiperiodic boundary value problem of the form \begin{equation*} ^C_{0}\Delta_{k}^{\alpha}x(k)=f\left(k+\alpha-1, x(k+\alpha-1)\right), \end{equation*} for $k\in[0,\ell+2]_{{N}_{0}}=\left\{0,1,...,\ell+2\right\}$, with boundary conditions $x(\alpha-3)=-x(\alpha+\ell)$, $\Delta x(\alpha-3)=-\Delta x(\alpha+\ell)$, $\Delta^{2} x(\alpha-3)=-\Delta^{2} x(\alpha+\ell)$, where $f: [\alpha-2, \alpha+\ell]_{{N}_{\alpha-2}}\times {R} \rightarrow {R}$ is continuous and $^C_{0}\Delta_{k}^{\alpha}$ is the Caputo fractional difference operator with order $2<\alpha \leq 3$. Finally, the main results are illustrated by suitable examples.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 33
Issue: 2
Year: 2020

DOI: 10.12732/ijam.v33i2.7

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