A New Fractional Representation of the Higher Order Taylor Scheme

Author:

Batiha Iqbal M.12ORCID,Jebril Iqbal H.1,Abdelnebi Amira3,Dahmani Zoubir4,Alkhazaleh Shawkat5ORCID,Anakira Nidal6

Affiliation:

1. Department of Mathematics, Al Zaytoonah University of Jordan, Amman 11733, Jordan

2. Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE

3. Laboratory of Pure and Applied Mathematics, Department of Mathematics, University of Mostaganem, Mostaganem, Algeria

4. Department of Mathematics, Laboratory LAMDA-RO, University of Blida 1, Blida 09000, Algeria

5. Department of Mathematics, Faculty of Science and Information Technology, Jadara University, Irbid, Jordan

6. Faculty of Education and Arts, Sohar University, Sohar 3111, Oman

Abstract

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.

Publisher

Hindawi Limited

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