Open Access

ARTICLE

A Novel Analytical Technique of the Fractional Bagley-Torvik Equations for Motion of a Rigid Plate in Newtonian Fluids

Mahmoud H. Taha¹, Mohamed A. Ramadan^2,*, Dumitru Baleanu^3,4,5, Galal M. Moatimid¹
1 Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt
2 Department of Mathematics & Computer Science, Faculty of Science, Menoufia University, Shebin El-Kom, Egypt
3 Department of Mathematics, Cankaya University, Ankara, 06530, Turkey
4 Institute of Atomic Physics, Magurele-Bucharest, 077125, Romania
5 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
* Corresponding Authors: Mohamed A. Ramadan. Email: ;

Computer Modeling in Engineering & Sciences 2020, 124(3), 969-983. https://doi.org/10.32604/cmes.2020.010942

Received 08 April 2020; Accepted 17 June 2020; Issue published 21 August 2020

Abstract

The current paper is concerned with a modified Homotopy perturbation technique. This modification allows achieving an exact solution of an initial value problem of the fractional differential equation. The approach is powerful, effective, and promising in analyzing some classes of fractional differential equations for heat conduction problems and other dynamical systems. To crystallize the new approach, some illustrated examples are introduced.

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Keywords

Bagley–Torvik equation; caputo sense; Riemann–Liouville integral; fractional differential equation

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