Analytic and numerical solutions of discrete Bagley–Torvik equation

Advances in Difference Equations

article

Meganathan, Murugesan¹  Abdeljawad, Thabet²  Motawi Khashan, M.⁵  Britto Antony Xavier, Gnanaprakasam¹  Jarad, Fahd⁶ 

[1] Department of Mathematics, Sacred Heart College (Autonomous);Department of Mathematics and General Sciences, Prince Sultan University;Department of Medical Research, China Medical University;Department of Computer Science and Information Engineering, Asia University;Department of Basic Sciences, King Saud University;Department of Mathematics, Çankaya University

关键词: Fractional calculus;    Difference operator;    Laplace transform;    Bagley–Torvik equation;    Caputo derivative;   

DOI  :  10.1186/s13662-021-03371-3

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this research article, a discrete version of the fractional Bagley–Torvik equation is proposed:1 $$ \nabla _{h}^{2} u(t)+A{}^{C} \nabla _{h}^{\nu }u(t)+Bu(t)=f(t),\quad t>0, $$ 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.

【 授权许可】

CC BY