Approximate solutions of fuzzy differential equations of fractional order using modified reproducing kernel Hilbert space method


Authors

Asia Khalaf Albzeirat - Institute of Engineering Mathematics, Universiti Malaysia Perlis, Pauh Putra Main Campus, 02600 Arau, Perlis, Malaysia. Muhammad Zaini Ahmad - Institute of Engineering Mathematics, Universiti Malaysia Perlis, Pauh Putra Main Campus, 02600 Arau, Perlis, Malaysia. Shaher Momani - Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan. - Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia. Norazrizal Aswad Abdul Rahman - Institute of Engineering Mathematics, Universiti Malaysia Perlis, Pauh Putra Main Campus, 02600 Arau, Perlis, Malaysia.


Abstract

In this paper, we use the modified reproducing kernel Hilbert space method to approximate the solution of fuzzy differential equations of fractional order. Using this method, we construct a new algorithm to approximate the solution of such differential equations. The proposed algorithm produces solutions in terms of interval-valued fuzzy numbers. Two numerical examples are tested and the results showed that the proposed algorithm is able to produce solutions that approach to the exact solutions. It concludes that the proposed algorithm can be considered as a modern algorithm that complements to the existing ones.


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ISRP Style

Asia Khalaf Albzeirat, Muhammad Zaini Ahmad, Shaher Momani, Norazrizal Aswad Abdul Rahman, Approximate solutions of fuzzy differential equations of fractional order using modified reproducing kernel Hilbert space method, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 5, 2423--2439

AMA Style

Albzeirat Asia Khalaf, Ahmad Muhammad Zaini, Momani Shaher, Rahman Norazrizal Aswad Abdul, Approximate solutions of fuzzy differential equations of fractional order using modified reproducing kernel Hilbert space method. J. Nonlinear Sci. Appl. (2017); 10(5):2423--2439

Chicago/Turabian Style

Albzeirat, Asia Khalaf, Ahmad, Muhammad Zaini, Momani, Shaher, Rahman, Norazrizal Aswad Abdul. "Approximate solutions of fuzzy differential equations of fractional order using modified reproducing kernel Hilbert space method." Journal of Nonlinear Sciences and Applications, 10, no. 5 (2017): 2423--2439


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