A New Fractional Representation of the Higher Order Taylor Scheme - Iqbal M. Batiha; Iqbal H. Jebril; Amira Abdelnebi; Zoubir Dahmani; Shawkat Alkhazaleh; Nidal Anakira (Computational and Mathematical Methods)
In this work, we suggest a new numerical scheme called the fractional higher order Taylor method (FHOTM) to solve fractional differential equations (FDEs). Using the generalized Taylor’s theorem is the fundamental concept of this approach. Then, the local truncation error generated by the suggested FHOTM is estimated by proving suitable theoretical results. At last, several numerical applications are given to demonstrate the applicability of the suggested approach in relation to their exact solutions.