Numerical Solutions of Fuzzy Fractional Variable-Order Differential Equations

Abstract

This paper addresses a class of fuzzy fractional differential equations (FFDEs) with variable-order (VO) derivatives, where the variable-order derivative is defined in the Caputo sense for fuzzy-valued functions. Using the $\Upsilon$-cut representation of fuzzy-valued functions, the original problem is reformulated into a new problem. To solve it, we apply operational matrices (OMs) derived from shifted Chebyshev polynomials of the third kind (SCP3). By approximating the unknown function and its derivative with SCP3, the problem is reduced to a system of nonlinear algebraic equations. A theoretical error analysis of the numerical solution is presented, along with an example to validate the method's accuracy.