On the numerical solutions of some fractional ordinary differential equations by fractional Adams-Bashforth-Moulton method

Haci Mehmet Baskonus; Hasan Bulut

Open Mathematics (2015)

  • Volume: 13, Issue: 1, page 4255-4270
  • ISSN: 2391-5455

Abstract

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In this paper, we apply the Fractional Adams-Bashforth-Moulton Method for obtaining the numerical solutions of some linear and nonlinear fractional ordinary differential equations. Then, we construct a table including numerical results for both fractional differential equations. Then, we draw two dimensional surfaces of numerical solutions and analytical solutions by considering the suitable values of parameters. Finally, we use the L2 nodal norm and L∞ maximum nodal norm to evaluate the accuracy of method used in this paper.

How to cite

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Haci Mehmet Baskonus, and Hasan Bulut. "On the numerical solutions of some fractional ordinary differential equations by fractional Adams-Bashforth-Moulton method." Open Mathematics 13.1 (2015): 4255-4270. <http://eudml.org/doc/275845>.

@article{HaciMehmetBaskonus2015,
abstract = {In this paper, we apply the Fractional Adams-Bashforth-Moulton Method for obtaining the numerical solutions of some linear and nonlinear fractional ordinary differential equations. Then, we construct a table including numerical results for both fractional differential equations. Then, we draw two dimensional surfaces of numerical solutions and analytical solutions by considering the suitable values of parameters. Finally, we use the L2 nodal norm and L∞ maximum nodal norm to evaluate the accuracy of method used in this paper.},
author = {Haci Mehmet Baskonus, Hasan Bulut},
journal = {Open Mathematics},
keywords = {Fractional Adams-Bashforth-Moulton method; Fractional calculus; Fractional nonlinear ordinary differential equation},
language = {eng},
number = {1},
pages = {4255-4270},
title = {On the numerical solutions of some fractional ordinary differential equations by fractional Adams-Bashforth-Moulton method},
url = {http://eudml.org/doc/275845},
volume = {13},
year = {2015},
}

TY - JOUR
AU - Haci Mehmet Baskonus
AU - Hasan Bulut
TI - On the numerical solutions of some fractional ordinary differential equations by fractional Adams-Bashforth-Moulton method
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - 4255
EP - 4270
AB - In this paper, we apply the Fractional Adams-Bashforth-Moulton Method for obtaining the numerical solutions of some linear and nonlinear fractional ordinary differential equations. Then, we construct a table including numerical results for both fractional differential equations. Then, we draw two dimensional surfaces of numerical solutions and analytical solutions by considering the suitable values of parameters. Finally, we use the L2 nodal norm and L∞ maximum nodal norm to evaluate the accuracy of method used in this paper.
LA - eng
KW - Fractional Adams-Bashforth-Moulton method; Fractional calculus; Fractional nonlinear ordinary differential equation
UR - http://eudml.org/doc/275845
ER -

References

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