Numerical Solution for Solving Nonlinear Fuzzy Fractional Integral Equation by Using Approximate Method

Authors

  • Alan Jalal Abdulqader Department of Mathematics, College of Education, Al-Mustansiriyah University, Baghdad, Iraq

Keywords:

fuzzy integral equation, fuzzy fractional integral equation, Riemann-liouville, successive approximate method.

Abstract

In this paper, we discus fractional order for fuzzy non-linear integral equation . The fractional integral is consider in the sense Riemann-liouville  and establish the exists solution  of nonlinear fuzzy fractional  integral equation. Finally, Numerical  examples are given to  illustrate the results.

References

A.M.A. El-Sayed, A.-G. Ibrahim, Set-valued integral equations of fractional-orders. Applied Mathematics and Computation 118 (2001), 113–121.

T. Allahviranloo, A. Armand and Z. Gouyandeh, Fuzzy fractional differential equations under generalized fuzzy Caputo derivative. Journal of Intelligent & Fuzzy Systems. 26 (2014), 1481- 1490.

B. Bede, Mathematics of fuzzy sets and fuzzy logic. Springer-Verlag Berlin Heidelberg (2013).

D. Baleanu, K. Diethelm, E. Scalas and J. J. Trujillo, Fractional Calculus Models and Numer- ical Methods, in: Series on Complexity, Nonlinearity and Chaos. World Scientific, Singapore, (2012).

K. Deimling, Nonlinear Functional Analysis. Springer–Verlag, Berlin– Heidelberg, 1985.

K. Diethelm, The Analysis of Fractional Differential Equations. Springer, 2004.

M. Amawi and N. Qatanani, Numerical Methods for Solving Fuzzy Fredholm Integral Equation of the Second Kind, International Journal of Applied Mathematics, Vol.28, No.3, 2015, 177-195 .

M. Dehghan, and B. Hashemi, Iterative Solution of Fuzzy Linear systems, Applied Mathematics and Computation, Vol. 175, 2006, 645-674

] P. Diamond, P. Kloeden, Metric Spaces of Fuzzy Sets. World Scientific, Singapore, 1994.

S. Arshad, on existence and uniqueness of solution of fuzzy fractional differential equations. Iranian Journal of Fuzzy Systems. Vol. 10. No. 6 (2013), 137–151.

W. Cong-xin, and M. Ming, Embedding problem of fuzzy number space: part 1, Fuzzy sets and systems, Vol. 44, Issue 1, 1991, 33-38.

Downloads

Published

2017-11-13

How to Cite

Abdulqader, A. J. (2017). Numerical Solution for Solving Nonlinear Fuzzy Fractional Integral Equation by Using Approximate Method. International Journal of Sciences: Basic and Applied Research (IJSBAR), 36(6), 8–17. Retrieved from https://www.gssrr.org/index.php/JournalOfBasicAndApplied/article/view/8345

Issue

Section

Articles