# Collocation method based on Chebyshev polynomials for solving distributed order fractional differential equations

Document Type : Research Paper

Authors

Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran.

Abstract

This work presents a new approximation approach to solve the linear/nonlinear distributed order fractional differential equations using the Chebyshev polynomials. Here, we use the Chebyshev polynomials combined with the idea of the collocation method for converting the distributed order fractional differential equation into a system of linear/nonlinear algebraic equations. Also, fractional differential equations with initial conditions can be solved by the present method. We also give the error bound of the modified equation for the present method. Moreover, four numerical tests are included to show the effectiveness and applicability of the suggested method.

Keywords

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### History

• Receive Date: 21 February 2020
• Revise Date: 11 June 2020
• Accept Date: 12 June 2020
• First Publish Date: 01 July 2021