An improved composite collocation method for distributed-order fractional differential equations based on fractional Chelyshkov wavelets

By Parisa Rahimkhani, Yadollah Ordokhani, P. Lima. Applied Numerical Mathematics, 2019

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Abstract In this paper, we introduce a new family of fractional functions based on Chelyshkov wavelets for solving one- and two-variable distributed-order fractional differential equations. The concept of fractional derivative is utilized in the Caputo sense. The idea of solving these problems is based on fractional integral operator of fractional-order Chelyshkov wavelets with composite collocation method. This operator and collocation method are utilized to reduce the solution of the distributed fractional differential equations to a system of algebraic equations. The convergence of the fractional-order Chelyshkov wavelets bases is discussed. The efficiency and the applicability of the new methodology are illustrated by eight examples, in addition our findings in comparison with the existing results show the advantage of our method.

Subfields: Control and Systems Engineering, Modeling and Simulation, Statistical and Nonlinear Physics

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