A novel operational vector for solving the general form of distributed order fractional differential equations in the time domain based on the second kind Chebyshev wavelets

Abstract

The main aim of this research study is to present a new and efficient numerical method based on the second kind Chebyshev wavelets for solving the general form of distributed order fractional differential equations in the time domain with the Caputo fractional derivatives. For the first time, based on the second kind Chebyshev wavelets, an exact formula for the operational vector of the Riemann-Liouville fractional integral operator is derived by using the unit step function and Laplace transform method. Applying this operational vector via the collocation method in our approach provides an approximate solution by converting the problem under consideration into a system of algebraic equations which can be solved by the Newton method. Discussion on the error bound and convergence analysis for the proposed method is presented. Finally, five test problems are considered to confirm the reliability and effectiveness of the proposed method.