Numerical solution method for multi-term variable order fractional differential equations by shifted Chebyshev polynomials of the third kind

Abstract

Multi-term variable-order fractional differential equations (VO-FDEs) are considered to be one of the tools to illustrate the behavior of transient-regime real-life phenomena precisely. The analytical solutions of VO-FDEs are generally very hard to obtain. Therefore, in this study, an approximation method for the solution of multi-term VO-FDEs is proposed using shifted Chebyshev polynomials of the third kind (SCP3). The method employs the operational matrices of SCP3 to proximate the VO-FDEs with a system of algebraic equations. The solution of which also yields the approximate result for the multi-term VO-FDE. An error analysis is also included. The SCP3 method is examined on several examples demonstrating the precision and prowess of the method.

Keywords

• Multi-term fractional differential equations
• Variable-order fractional differential equations
• Shifted Chebyshev polynomials of the third kind
• Operational matrix method