Finance

Orthogonal polynomials

Matrix (chemical analysis)

Legendre polynomials

Physics

Mathematical analysis

Legendre function

Nonlinear system

Economics

Order (exchange)

Variable (mathematics)

Chemistry

Collocation method

Classical orthogonal polynomials

Algebraic equation

Applied mathematics

Mathematics

Associated Legendre polynomials

Chromatography

Numerical analysis

Ordinary differential equation

Quantum mechanics

Differential equation

Gegenbauer polynomials

Mathematical Methods in the Applied Sciences

In this paper, shifted Legendre polynomials will be used for constructing the numerical solution for a class of multiterm variable‐order fractional differential equations. In the proposed method, the shifted Legendre operational matrix of the fractional variable‐order derivatives will be investigated. The fundamental problem is reduced to an algebraic system of equations using the constructed matrix and the collocation technique, which can be solved numerically. The error estimate of the proposed method is investigated. Some numerical examples are presented to prove the applicability, generality, and accuracy of the suggested method.

Numerical solution of multiterm variable‐order fractional differential equations via shifted Legendre polynomials