Engineering with Computers ( IF 3.938 ) Pub Date : 2020-10-16 , DOI: 10.1007/s00366-020-01192-8 Faezeh Sadat Yousefi, Yadollah Ordokhani, Sohrabali Yousefi
In this paper, we present a new numerical method for solving variable order fractional differential equations, which is based on shifted Legendre cardinal functions. First, we obtain the pseudo-operational matrix of the variable order fractional derivative by applying the properties mentioned in the Caputo derivative of fractional variable order. Then, using Ritz method, the pseudo-operational matrix and collocation method, the problem is reduced to a system of algebraic equations that is solved by Newton’s iterative method. Illustrative examples are included to demonstrate the efficiency and accuracy of the proposed method.