IJPAM: Volume 115, No. 3 (2017)

Title

AN APPROPRIATE METHOD TO HANDLE
FUZZY INTEGRO-DIFFERENTIAL EQUATIONS

Authors

S.P. Sathiyapriya$^1$, S. Narayanamoorthy$^2$
$^{1,2}$Department of Mathematics
Bharathiar University
Coimbatore, 641046, Tamil Nadu, INDIA

Abstract

Several mathematical formulations of physical phenomena under uncertainty contain fuzzy integro-differential equations and due to their frequent appearance in several applied fields, an appropriate method for handling them is presented. Our proposed algorithm is given in detail and it can be treated as the extended form of homotopy perturbation method. We use an accelerating parameter to enhance the rate of convergence of the solution and construction of suitable homotopy facilitates the calculation of approximate solution in the form of convergent series with simple computable components.

History

Received: April 29, 2017
Revised: June 20, 2017
Published: July 27, 2017

AMS Classification, Key Words

AMS Subject Classification: 03B52, 45B02
Key Words and Phrases: fuzzy integro-differential equation, homotopy perturbation method, accelerating parameter, approximate solution

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Bibliography

1
T. Allahviranloo, S. Abbasbandy and S. Hashemzehi, Approximating the solution of the linear and nonlinear fuzzy Volterra integrodifferential equations using expansion method, Abstract and Applied Analysis, Article ID 713892, 2014 (2014), 1-7.

2
D. Dubois and H. Prade, Towards fuzzy differential calculus, Fuzzy Sets and Systems, 8 (1982), 1-7.

3
O. Ghasemi, M. Tavassoli Kajani and E. Babolian, Application of He's homotopy perturbation method to nonlinear integro-differential equations, Applied Mathematics and Computation, 188 (2007), 538-548.

4
R. Goetschel, W. Voxman, Elementary fuzzy calculus, Fuzzy Sets and Systems, 18 (1986), 31-43.

5
J. H. He, Homotopy perturbation technique, Comput Methods Appl Mech Engrg, 178 (1999), 257-262.

6
J. H. He, A coupling method of a homotopy technique and a perturbation technique for non-linear problems, International Journal of Non-Linear Mechanics, 35 (2000), 37-43.

7
O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems, 24, No. 2 (1987), 301- 317.

8
S. Narayanamoorthy and S. P. Sathiyapriya, Homotopy perturbation method: a versatile tool to evaluate linear and nonlinear fuzzy Volterra integral equations of the second kind, SpringerPlus, 5, 387 (2016), 1-16, doi: https://doi.org/10.1186/s40064-016-2038-3.

9
S. Narayanamoorthy and S. P. Sathiyapriya, A pertinent approach to solve nonlinear fuzzy integro-differential equations, SpringerPlus, 5:449 (2016), 1-17, doi: https://doi.org/10. 1186/s4006401620454.

10
J. Saberi-Nadjafi and A. Ghorbani, He’s homotopy perturbation method: An effective tool for solving integral and integro-differential equations, Computers and Mathematics with Appications, 58 (2009), 2379-2390.

11
L. A. Zadeh, Fuzzy Sets, Information and Control, 8 (1965), 338-353.

How to Cite?

DOI: 10.12732/ijpam.v115i3.8 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 115
Issue: 3
Pages: 539 - 548


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