If we apply the technique described in the 'Application of Laguerre operational matrix for multi- order FDEs' subsection with N=3, then the approximate solution can be written as follows: u N ( x ) = ∑ i = 0 3 c i L i ( x ) = C T ϕ ( x ), Open image in new window.
Several different types of nonlinear examples are given to illustrate the scope and demonstrate the validity of our software package, especially for nonlinear multi-order and multi-point boundary value problems.
Moreover the treatment of the nonlinear multi-order fractional multi-point value problems; with leading fractional-differential operator of order ν (m - 1 < ν ≤ m), on the interval [0, t] is described, by shifted Legendre collocation (SLC) method to find the solution u N (x).
We also present a Gauss-Lobatto shifted Legendre collocation method for solving nonlinear multi-order FDEs with multi-point boundary conditions.
In this section, we use the shifted Legendre collocation method to numerically solve the nonlinear multi-order FDE with multi-point boundary conditions, namely D ν u ( x ) = F ( x, u ( x ), D δ 1 u ( x ), …, D δ k u ( x ) ), x ∈ I, (41).
In Section 3, we consider the SLT method for the multi-term FDEs subject to multi-point boundary conditions, and in Section 4, we construct an algorithm for solving linear multi-order FDEs with variable coefficients subject to multi-point boundary conditions by using the Q-SLT method.
Also we provide a way to choose the index when facing multi-order problems.
In the 'Application of Laguerre operational matrix for multi-order FDEs' subsection of the 'Methods' section, we apply the Laguerre operational matrix of fractional integration for solving linear multi-order FDEs.
In Section 4, we apply the modified generalized Laguerre operational matrix of fractional integration to solve linear multi-order FDEs.
With features like indoor mapping and multi-order picking, the platform also helps grocery stores manage the packing and prepping of customers' orders.
Jafari in [39] used the HAM to obtain the solution of multi-order fractional differential equation studied by Diethelm and Ford [40].
