Abstract
In this research article, a discrete version of the fractional Bagley–Torvik equation is proposed: 1∇h2u(t)+AC∇hνu(t)+Bu(t)=f(t),t>0,\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$ \\nabla _{h}^{2} u(t)+A{}^{C} \\nabla _{h}^{\\nu }u(t)+Bu(t)=f(t),\\quad t>0, $$\\end{document} where 0<nu <1 or 1<nu <2, subject to u(0)=a and nabla _{h} u(0)=b, with a and b being real numbers. The solutions are obtained by employing the nabla discrete Laplace transform. These solutions are expressed in terms of Mittag-Leffler functions with three parameters. These solutions are handled numerically for some examples with specific values of some parameters.
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