Numerical Studied for Solving Fuzzy Integro-Differential Equations via Caputo Fractional Derivative

Authors

  • Ruaa N. Abduallah
  • Rokan khaji

DOI:

https://doi.org/10.24237/ASJ.02.04.780B

Keywords:

Euler method, exact solution, approximate solution, fuzzy parameter, Caputo Fractional.

Abstract

In this paper, we extended some numerical methods to solve fuzzy integro differential equations. The considered problem involves the fractional Caputo derivatives under some conditions on the ordered. As we combine Euler's method with composite Simpsons have been used to determine the solutions of these equations. We extend these numerical techniques to find the best solutions. Extended difference Euler technique is used for this. The results show that the extended Euler method is more accurate in terms of absolute error. Illustrative examples are given to demonstrate the high precision and good performance of the new class.

References

C. E. Shanon, A mathematical Theory of Communication, Bell systems technology j., 27, 379-423(1948)

S. Seikkala, On the fuzzy initial value problem, Fuzzy sets and systems, 24(3), 319-330(1987)

D. Dubois, H. Prade, Towards fuzzy differential calculus part 1: Integration of fuzzy mappings, Fuzzy sets and Systems, 8(1), 1-17(1982)

O. Kaleva, The Cauchy problem for fuzzy differential equations, Fuzzy sets and systems, 35(3), 389-396(1990)

S. Hajighasemi, T. Allahviranloo, M. Khezerloo, M. Khorasany, S. Salahshour, Existence and uniqueness of solutions of fuzzy Volterra integro-differential equations, In: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications: 13th International Conference, IPMU 2010, Dortmund, Germany, June 28–July 2, 2010. Proceedings, Part II 13, Springer Berlin Heidelberg, 491-500 (2010)

F. Ishak, N. Chaini, Numerical computation for solving fuzzy differential equations, Indonesian Journal of Electrical Engineering and Computer Science, 16(2), 1026-1033(2019)

S. S. Chang, L. A. Zadeh, On fuzzy mapping and control, IEEE Transactions on Systems, Man, and Cybernetics, (1), 30-34(1972)

R. Goetschel Jr, W. Voxman, Fuzzy circuits, Fuzzy Sets and Systems, 32(1), 35-43(1989)

Y. Chalco-Cano, H. Roman-Flores, On new solutions of fuzzy differential equations, Chaos, Solitons & Fractals, 38(1), 112-119(2008)

R. Bello, R. Falcon, J. L. Verdegay, (Eds.), Uncertainty management with fuzzy and rough sets: Recent advances and applications, (2019)

D. Dubois, H. Prade, (Eds.), Fundamentals of fuzzy sets (Vol. 7), (Springer Science & Business Media, 2012).

P. Darabi, S. Moloudzadeh, H. Khandani, A numerical method for solving first-order fully fuzzy differential equation under strongly generalized H-differentiability, Soft Computing, 20, 4085-4098(2016)

S. Bhalekar, Dynamics of fractional order complex Ucar system, In Fractional Order Control and Synchronization of Chaotic Systems, (Springer, Cham, 2017), 747–771

I. Podlubny, Fractional Differential Equations, (Academic Press, New York, 2009)

M. P. Velasco, D. Usero, S. Jiménez, L. Vázquez, J. L. Vázquez-Poletti, M. Mortazavi, About some possible implementations of the fractional calculus, Mathematics, 8(6), 893(2020)‏

D. Usero, Fractional Taylor series for Caputo fractional derivatives, Construction of numerical schemes, (2008)

L. Kexue, P. Jigen, Laplace transform and fractional differential equations, Applied Mathematics Letters, 24(12), 2019-2023(2011)

N. Ahmad, A. Ullah, S. Ahmad, K. Shah, I. Ahmad, On analysis of the fuzzy fractional order Volterra-Fredholm integro-differential equation, Alexandria Engineering Journal, 60(1), 1827-1838(2021)‏

M. R. M. Shabestari, R. Ezzati, T. Allahviranloo, Numerical solution of fuzzy fractional integro-differential equation via two-dimensional Legendre wavelet method, Journal of Intelligent & Fuzzy Systems, 34(4), 2453-2465(2018)

Downloads

Published

2024-10-01

How to Cite

Ruaa N. Abduallah, & Rokan khaji. (2024). Numerical Studied for Solving Fuzzy Integro-Differential Equations via Caputo Fractional Derivative. Academic Science Journal, 2(4), 228–240. https://doi.org/10.24237/ASJ.02.04.780B

Issue

Section

Articles