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Error Analysis between Runge Kutta Fourth Order Method & Fehlberg 6th Order Method of Hybrid Fuzzy Fractional Differential Equations

M. Saradha1 , S. Ruban Raj2

  1. Department of Mathematics, MVJ College of Engineering, Bangalore, India.
  2. Department of Mathematics, St.Joseph College, Trichirappalli, India.

Section:Research Paper, Product Type: Isroset-Journal
Vol.5 , Issue.3 , pp.24-33, Jun-2018


CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i3.2433


Online published on Jun 30, 2018


Copyright © M. Saradha , S. Ruban Raj . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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IEEE Style Citation: M. Saradha , S. Ruban Raj, “Error Analysis between Runge Kutta Fourth Order Method & Fehlberg 6th Order Method of Hybrid Fuzzy Fractional Differential Equations,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.3, pp.24-33, 2018.

MLA Style Citation: M. Saradha , S. Ruban Raj "Error Analysis between Runge Kutta Fourth Order Method & Fehlberg 6th Order Method of Hybrid Fuzzy Fractional Differential Equations." International Journal of Scientific Research in Mathematical and Statistical Sciences 5.3 (2018): 24-33.

APA Style Citation: M. Saradha , S. Ruban Raj, (2018). Error Analysis between Runge Kutta Fourth Order Method & Fehlberg 6th Order Method of Hybrid Fuzzy Fractional Differential Equations. International Journal of Scientific Research in Mathematical and Statistical Sciences, 5(3), 24-33.

BibTex Style Citation:
@article{Saradha_2018,
author = {M. Saradha , S. Ruban Raj},
title = {Error Analysis between Runge Kutta Fourth Order Method & Fehlberg 6th Order Method of Hybrid Fuzzy Fractional Differential Equations},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {6 2018},
volume = {5},
Issue = {3},
month = {6},
year = {2018},
issn = {2347-2693},
pages = {24-33},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=669},
doi = {https://doi.org/10.26438/ijcse/v5i3.2433}
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
DO = {https://doi.org/10.26438/ijcse/v5i3.2433}
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=669
TI - Error Analysis between Runge Kutta Fourth Order Method & Fehlberg 6th Order Method of Hybrid Fuzzy Fractional Differential Equations
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - M. Saradha , S. Ruban Raj
PY - 2018
DA - 2018/06/30
PB - IJCSE, Indore, INDIA
SP - 24-33
IS - 3
VL - 5
SN - 2347-2693
ER -

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Abstract :
In this paper we study Error analysis of numerical methods for second order hybrid fuzzy fractional differential equations. We solve the hybrid fuzzy fractional differential equations with a fuzzy initial condition by using variational iteration method. We consider a second order differential equation with fractional values and we compared the results with their exact solutions in order to demonstrate the validity and applicability of the method. We further give the definition of the Degree of Sub element hood of hybrid fuzzy fractional differential equations with examples.

Key-Words / Index Term :
Hybrid fuzzy fractional differential equations, Degree of Sub Element hood, Runge Kutta Fehlberg 6th order Method

References :
[1] Arshad, S, Lupulescu, V, “Fractional differential equation with the fuzzy initial condition”, Electron. J. Differ. Equ. 34, 1-8 (2011)
[2] Agarwal, RP, Lakshmikanthama, V, Nieto. JJ, “On the concept of solution for fractional differential equations with uncertainty”, Nonlinear Anal. 72, 2859-2862 (2010)
[3] Ekhtiar Khodadadi and Ercan Çelik, “The variational iteration method for fuzzyfractional differential equations with uncertainty”, Fixed Point Theory and Applications 2013, 2013:13
[4] K. Miller and B. Ross, “An introduction to the fractional calculus and fractional differential equations”, Wiley, New York, 1993.
[5] M. Z. Ahmad and M. K. Hasan, “Numerical methods for fuzzy initial value problems under different types of interpretation: a comparison study,” in Informatics Engineering and Information Science, vol. 252 of Communications in Computer and Information Science, pp. 275–288, Springer, Berlin, Germany, 2011.
[6] S. Pederson and M. Sambandham, “Numerical solution to hybrid fuzzy systems”, Mathematical and Computer Modelling 45 (2007), 1133–1144.
[7] S. Ruban Raj, M. Saradha, “Properties of Fuzzy Soft Set”, International Journal for Basic Sciences and Social Sciences (IJBSS), ISSN:2319-2968, 2(1) (2013), pp.112-118.
[8] S. Ruban Raj, M. Saradha, “Solving Hybrid Fuzzy Fractional Differential Equation By Modified Euler Method”, Annexure II of Anna University-2014 and ICMAA–2014. 550-560.
[9]. S. Ruban Raj, M. Saradha, “Solving Second Order Hybrid Fuzzy Fractional Differential Equation By Runge Kutta Fourth Order Method”, International Journal of Science and Research, ISSN (Online): 2319-7064, Volume4, Issue 1, January 2015.
[10] S. Ruban Raj, M. Saradha, “Solving Hybrid Fuzzy Fractional Differential Equation By Runge Kutta Fourth Order Method”, International Journal of Science and Research, ISSN (Online): 2319-7064, Volume4, Issue 2, February 2015.

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