NON-OSCILLATORY BEHAVIOR OF HIGHER ORDER HILFER FRACTIONAL DIFFERENCE EQUATION | ||
| Journal of Fractional Calculus and Applications | ||
| Volume 15, Issue 2, July 2024, Pages 1-9 PDF (222.25 K) | ||
| Document Type: Regular research papers | ||
| DOI: 10.21608/jfca.2024.273085.1070 | ||
| Authors | ||
| Sivakumar Arundhathi1; Velu Muthulakshmi* 2 | ||
| 1Department of Mathematics, Periyar University, Salem-636 011, Tamilnadu, India | ||
| 2Department of Mathematics, Periyar University, Salem, Tamil Nadu, India | ||
| Abstract | ||
| In this paper, we look into the non-oscillatory behavior of the higher order forced fractional difference equation with positive and negative terms. Since the fractional difference and summation feature has considerably demonstrated its efficiency and validity due to its nonlocal nature and memory interpretation, we employ the Hilfer fractional difference operator, which is an extension of the most widely used Riemann-Liouville and Caputo fractional difference operators. Unlike the method that has been used in the literature, our study is based on certain fundamental concepts derived from discrete fractional calculus as well as mathematical inequalities. In order to aid in arriving at the important end result, a Volterra-type summation equation is constructed as a similar representation of our higher order Hilfer fractional difference problem. We were able to come up with new, easier to implement condition that were satisfied by the non-oscillatory solutions to our analyzed Hilfer fractional difference equation. Further, to demonstrate the empirical reliability of the theoretical finding, we lend a numerical example. | ||
| Keywords | ||
| Hilfer difference operator; non-oscillation criteria; mathematical inequalities; fractional difference equations | ||
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