Abstract
In this paper, we propose an efficient method for constructing numerical algorithms for solving the fractional initial value problem by using the Pade approximation of fractional derivative operators. We regard the Grunwald–Letnikov fractional derivative as a kind of Taylor series and get the approximation equation of the Taylor series by Pade approximation. Based on the approximation equation, we construct the corresponding numerical algorithms for the fractional initial value problem. Finally, we use some examples to illustrate the applicability and efficiency of the proposed technique.
Highlights
Fractional differential equations were successfully applied to many problems in engineering, physics, chemistry, biology, economics, control theory, biophysics, and so on [1,2,3,4,5]
We propose an efficient method for constructing numerical algorithms for solving the fractional initial value problem by using the Pade approximation of fractional derivative operators. e advantage of the proposed technique is that efficient numerical methods can be constructed without calculation of long historical terms of the fractional derivative
Pade approximation [21] is believed to be the best approximation of a function by rational functions of a given order
Summary
Fractional differential equations were successfully applied to many problems in engineering, physics, chemistry, biology, economics, control theory, biophysics, and so on [1,2,3,4,5]. We propose an efficient method for constructing numerical algorithms for solving the fractional initial value problem by using the Pade approximation of fractional derivative operators. E advantage of the proposed technique is that efficient numerical methods can be constructed without calculation of long historical terms of the fractional derivative. Algorithm 5 is a technique which is easy to manipulate This method involves huge computational work when T ≫ 0 because in general, these methods need to compute many terms to get the approximation to the fractional derivative. We put forward a reliable method for the construction of numerical algorithms for solving the fractional differential initial value problem by using Pade approximation to fractional derivative operators.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
