An Operational Matrix Based on Legendre Polynomials for Solving Fuzzy Fractional-Order Differential Equations

Abstract

This paper deals with the numerical solutions of fuzzy fractional differential equations under Caputo-type fuzzy fractional derivatives of order $\alpha \in \left(\mathrm{0,1}\right)$. We derived the shifted Legendre operational matrix (LOM) of fuzzy fractional derivatives for the numerical solutions of fuzzy fractional differential equations (FFDEs). Our main purpose is to generalize the Legendre operational matrix to the fuzzy fractional calculus. The main characteristic behind this approach is that it reduces such problems to the degree of solving a system of algebraic equations which greatly simplifies the problem. Several illustrative examples are included to demonstrate the validity and applicability of the presented technique.