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Numerical solution of the fractional Bagley‐Torvik equation by using hybrid functions approximation
Author(s) -
Mashayekhi Somayeh,
Razzaghi Mohsen
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3486
Subject(s) - mathematics , operator (biology) , boundary value problem , algebraic equation , fractional calculus , numerical analysis , mathematical analysis , biochemistry , chemistry , physics , repressor , nonlinear system , quantum mechanics , transcription factor , gene
In this paper, a new numerical method for solving the fractional Bagley‐Torvik equation is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block‐pulse functions and Bernoulli polynomials are presented. The Riemann‐Liouville fractional integral operator for hybrid functions is introduced. This operator is then utilized to reduce the solution of the initial and boundary value problems for the fractional Bagley‐Torvik differential equation to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. Copyright © 2015 John Wiley & Sons, Ltd.