Abstract
We study a fuzzy fractional differential equation (FFDE) and present its solution using Zadeh's extension principle. The proposed study extends the case of fuzzy differential equations of integer order. We also propose a numerical method to approximate the solution of FFDEs. To solve nonlinear problems, the proposed numerical method is then incorporated into an unconstrained optimisation technique. Several numerical examples are provided.
Highlights
Fractional calculus is an important branch in mathematical analysis
We study a fuzzy fractional differential equation (FFDE) and present its solution using Zadeh’s extension principle
We propose a new interpretation of fuzzy fractional differential equations and present their solutions analytically and numerically
Summary
Fractional calculus is an important branch in mathematical analysis. It is a generalisation of ordinary calculus that allows noninteger order. The well-known and popularly used method in solving fractional differential equations is the Caputo fractional derivative It allows to specify a quantity of integer order derivatives at the initial point. In order to obtain a more realistic model than (1), Agarwal et al [31] have taken an initiative to introduce the concept of solution for fuzzy fractional differential equations. This contribution has motivated several authors to establish some results on the existence and uniqueness of solution (see [32]). The authors considered fuzzy fractional differential equations under the Riemann-Liouville H-derivative It requires a quantity of fractional H-derivative of an unknown solution at the fuzzy initial point.
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