Approximate solutions of fuzzy differential equations of fractional order using modified reproducing kernel Hilbert space method. (English) Zbl 1412.34007
Summary: 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.
MSC:
| 34A08 | Fractional ordinary differential equations |
| 34A07 | Fuzzy ordinary differential equations |
| 47B32 | Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) |
Keywords:
Caputo fractional derivative; fuzzy differential equation of fractional order; modified reproducing kernel Hilbert space methodReferences:
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