Numerical solution of Bagley–Torvik equation including Atangana–Baleanu derivative arising in fluid mechanics

Abstract

Differential equations involving fractional order operators appear frequently in various research areas. Solving a differential equation containing a fractional derivative is very difficult. In this article, our aim is to solve Bagley–Torvik equation involving Atangana–Baleanu derivative using Laplace transform method. Laplace transform is an effective tool in engineering and other science subjects for solving differential equations. However, using the Laplace transform method sometimes leads to solutions in the Laplace domain that cannot be inverted back to the time domain by analytical methods. Therefore, numerical methods are then used to convert the solution from Laplace domain to time domain. In this work, four numerical inverse Laplace transform methods are utilized. Four test problems are considered to validate the accuracy and efficiency of the proposed numerical methods. The computational results are illustrated with the help of tables and figures. In order to show the superiority of the methods the obtained results are compared with other methods available in literature.