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Solving fuzzy fractional differential equations using Zadeh's extension principle
M Z Ahmad1, M K Hasan, S Abbasbandy
1Institute of Engineering Mathematics, Universiti Malaysia Perlis, Kampus Tetap Pauh Putra, 02600 Arau, Perlis, Malaysia.
Thescientificworldjournal
|October 2, 2013
Summary
This study introduces a novel method for solving fuzzy fractional differential equations (FFDEs) using Zadeh's extension principle. A new numerical technique is proposed for approximating FFDE solutions, extending previous work on integer-order fuzzy differential equations.
Area of Science:
- Mathematics
- Numerical Analysis
- Fuzzy Mathematics
Background:
- Fuzzy differential equations (FDEs) are an extension of classical differential equations to model uncertainty.
- Fractional calculus extends the concept of differentiation and integration to non-integer orders.
- Existing methods for fuzzy differential equations primarily focus on integer orders.
Purpose of the Study:
- To introduce and solve fuzzy fractional differential equations (FFDEs).
- To extend the theory of fuzzy differential equations to fractional orders.
- To develop and validate a numerical method for FFDEs.
Main Methods:
- Zadeh's extension principle is utilized for solving the FFDE.
- A novel numerical method is proposed for approximating FFDE solutions.
- The numerical method is integrated with unconstrained optimization for nonlinear problems.
Main Results:
- The study successfully presents a framework for solving FFDEs.
- A new numerical approximation technique for FFDEs is demonstrated.
- Numerical examples validate the effectiveness of the proposed method.
Conclusions:
- The proposed approach effectively extends the solution of fuzzy differential equations to fractional orders.
- The developed numerical method provides a viable tool for approximating FFDE solutions.
- The integration with optimization techniques enhances the applicability to nonlinear FFDEs.
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