Computation of numerical solutions to variable order fractional differential equations by using non-orthogonal basis

Abstract

In this work, we present some numerical results about variable order fractional differential equations (VOFDEs). For the said numerical analysis, we use Bernstein polynomials (BPs) with non-orthogonal basis. The method we use does not need discretization and neither collocation. Hence omitting the said two operations sufficient memory and time can be saved. We establish operational matrices for variable order integration and differentiation which convert the consider problem to some algebraic type matrix equations. The obtained matrix equations are then solved by Matlab 13 to get the required numerical solution for the considered problem. Pertinent examples are provided along with graphical illustration and error analysis to validate the results. Further some theoretical results for time complexity are also discussed.

Keywords

• non-orthogonal basis
• vofdes
• operational matrices
• algebraic matrix equation