Chebyshev operational matrix method for solving multi-order fractional ordinary differential equations

Shifted fractional-order Jacobi orthogonal functions: Application to a system of fractional differential equations

“…(6.5) into a system of FDEs by changing variable y 1 (x) = y(x) gives method, see [51] with various choices of x. Therefore, this example indicates that the obtained numerical results are very accurate and that the SFJCM is compared favorably with the COM [51]. Table 6.7…”

“…Example 4. In the last example, we consider the following nonlinear fractional differential equation [51] x 7 2 D 3 2 y(x) + D 2 y(x) + y 2 (x) = (1 + 4 √ π )x 4 + 2, y(0) = 0, y (0) = 0, (6.6)…”

A method based on the Jacobi tau approximation for solving multi-term time–space fractional partial differential equations

“…Operational matrices are used in several areas of numerical analysis and they hold particular importance for solving different kinds of problems in various subjects such as differential equations [47,48], integral equations [49], integro-differential equations [50,51], ordinary and partial fractional differential equations [52,53,54,55], optimal control problems [56] and etc.…”

Programming Variational Iteration Method via Wolfram-Mathematica for Solving Multi-Order Differential Equations

“…one part of this important equations is multi-order differential equations. Many researchers have studied this kind of differential equations by using different ways and methods, such as: generalized sine-cosine wavelets [13], Boubaker polynomials [1], homotopy analysis method [3], Legendre pseudo-spectral method [14], Chebyshev operational matrix method [4], and wavelet collocation method [5], Other related studies are on: modified HPM for solving generalized linear complex differential equations [9], solving fractional differential equations using Haar wavelet techniques [11], studies on the mathematical model of HIV infection of CD + 4 T by using HPM and VIM [2], studies of general second-order partial differential equations using HPM [6], of general first-order partial differential equations using HPM [7], and solving generalized Riccati differential equation [8]. One of the most popular methods for solving equations is variational iteration (VIM), and in the present work we use this method for solving a class of multi-order ordinary differential equation.…”