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A numerical algorithm for the solution of nonlinear fractional differential equations via beta‐derivatives
Author(s) -
Hatipoğlu Veysel Fuat
Publication year - 2018
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.5305
Subject(s) - mathematics , fractional calculus , nonlinear system , collocation method , sinc function , convergence (economics) , derivative (finance) , mathematical analysis , order (exchange) , differential equation , ordinary differential equation , physics , quantum mechanics , economic growth , financial economics , economics , finance
In this paper, the sinc‐collocation method (SCM) is investigated to obtain the solution of the nonlinear fractional order differential equations based on the relatively new defined fractional derivative, beta‐derivative. For this purpose, a theorem is proved for the approximate solution obtained from the SCM. Moreover, convergence analysis of the SCM is presented. To show the efficiency and the simplicity of the proposed method, some examples are solved, and the results are compared with the exact solutions of the considered equations.