Bessel collocation method for solving variable order fractional problems

n this paper, we examined a wide class of the variable order fractional problems such as linear and nonlinear fractional variable order differential equations, variable order fractional functional boundary value problems, variable order fractional pantograph differential equations. The proposed method is a collocation method based on the Bessel polynomials and the operational matrix of derivatives, which transformed equations into a system of non-linear algebraic equations to achieve the approximate solution. By using Caputo fractional derivative, the operational matrix of the variable-order fractional derivatives is constructed. The error analysis shows that the method is convergent. Several numerical results confirm the accuracy and efficiency of the proposed method