Fractional Jacobi operational matrix for solving Fuzzy Fractional Differential Equation1

Analytical solutions of linear inhomogeneous fractional differential equation with continuous variable coefficients

“…, n 0 -1), we find the jth element y j (t) of the canonical system. From (11) and (12), the first approximation of y j (t) is given by…”

“…Proof Let find the canonical system as the limit of the approximation sequence (11) and (12). Fixing j = 0, 1, .…”

“…Currently, methods for solving FDEs with initial conditions can be classified into two classes, namely, approximative method and analytical methods. Typical approximative methods include the operational matrix method based on orthogonal functions, the predictor-corrector method, fractional Euler method, and so on ( [11][12][13][14][15][16]). The most practical analytical methods are the Adomian decomposition method, the homotopy analysis method, the homotopy perturbation method, the Laplace transform method, and the variational iteration method ( [17][18][19][20][21]).…”

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].…”