Using the fuzzy center method to solve linear fractional fuzzy differential equations of order n with initial conditions
Keywords:
fuzzy centre, based methods, fuzzy fractional derivatives caputo, type, fuzzy number, fuzzy fractional linear differential equations, mittag-leffler functionAbstract
Fuzzy fractional differential equations (FFDEs) provide a powerful mathematical framework for modeling dynamic systems characterized by uncertainty in data, parameters, and initial conditions. This research aims to develop an analytical methodology for solving linear FFDEs of order n using the Fuzzy Centre Method (FCM). The proposed approach transforms the original fuzzy equation into a classical differential equation through the concept of the fuzzy centre, then applies Laplace transforms for the Caputo fractional derivative to obtain the solution, which is subsequently reconstructed into a complete fuzzy solution.
Three distinct cases of coefficients are considered: all positive, all negative, and mixed signs. Numerical examples demonstrate that the solutions obtained by FCM are in excellent agreement with the exact solutions at r=1, and also closely match results derived from alternative approaches such as the Addition and Subtraction of Fuzzy Numbers Method (ASFM).
The findings confirm that FCM is both reliable and flexible in handling various scenarios, with numerical validation carried out in MATLAB to support its accuracy and computational efficiency. This highlights the method’s robustness in addressing fuzzy fractional initial value problems and its ability to provide consistent results across different coefficient structures.
The study concludes that the FCM offers a strong and systematic framework for solving FFDEs and recommends extending its application to nonlinear fuzzy fractional differential equations and multi-variable fuzzy fractional systems. Furthermore, potential applications in engineering, economics, and life sciences are highlighted, where uncertainty is an inherent feature of mathematical modeling.
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