Modified Chebyshev wavelet methods for fractional delay-type equations

Abstract

In this article, we develop the Chebyshev wavelet method for solving the fractional delay differential equations and integro-differential equations. According to the development, we approximate the delay unknown functions by the Chebyshev wavelets series at delay time, which we call the delay Chebyshev wavelet series. We also proposed a technique by combining the method of steps and Chebyshev wavelet method for solving fractional delay differential equations. This technique converts the fractional delay differential equation on a given interval to a fractional non-delay differential equation over that interval, by using the function defined on previous interval, and then apply the Chebyshev wavelet method on the obtained fractional non-delay differential equation to find the solution. Numerical examples will be presented to demonstrate the benefits of computing with these approaches.