Application of a spectral method to Fractional Differential Equations under uncertainty1

A Review on Fuzzy Differential Equations

“…Although solving FFDEs under the concept of Riemann-Liouville H-derivative has been investigated by some proposed methods such as fuzzy Laplace transform method [118] and Mittag-Leffler functions [180], Caputo Hderivative and Caputo gH-derivative have been more palatable concepts of fuzzy fractional derivatives that have triggered much research work. Hence, by the consideration of such fuzzy fractional derivatives, some of the methods dedicated to obtain solutions of FFDEs are modified fractional Euler method [121], spline collocation method [181], Chebyshev polynomials [182], differential transform method [183], spectral method [184], [185], residual power series [186], perturbation-iteration algorithm [187].…”

Existence and Continuous Dependence on Initial Data of Solution for Initial Value Problem of Fuzzy Multiterm Fractional Differential Equation

“…The analytical method includes the Laplace transform method, monotone iterative method, variation of constant formula, and so on [13][14][15]. Typical numerical methods are the operational matrix method, fractional Euler method, predictor-corrector method, and so on [16][17][18][19][20][21].…”

Constructive Existence of (1,1)-Solutions to Two-Point Value Problems for Fuzzy Linear Multiterm Fractional Differential Equations

“…Currently, the approximative methods for solving fuzzy fractional differential equation include the operational matrix method based on orthogonal functions [8][9][10], linearization formula [11], Homotopy Analysis Method [12][13][14], and Variation of constant formula [15].…”