Taylor's expansion for fractional matrix functions: theory and applications

Volume 21, Issue 1, pp 1--17 http://dx.doi.org/10.22436/jmcs.021.01.01

Publication Date: March 10, 2020 Submission Date: August 07, 2019 Revision Date: January 23, 2020 Accteptance Date: February 04, 2020

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Authors

Ahmad El-Ajou - Department of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, Jordan. - Department of Mathematics, Faculty of Science, Taibah University, Madina, KSA.

Abstract

In this paper, several aims and tasks have been accomplished that can be summarized in the following points. Firstly, we recover some nice results related to the convergence and radii of convergence for the matrix fractional power series formula. Secondly, the Frobenius norm approximations for the matrix fractional derivatives in Caputo sense and fractional integrals in Riemann-Liouville sense are presented. Thirdly, we present the general exact and numerical solutions of four important and interesting matrix fractional differential equations and a new computational technique is also applied for getting the general solutions of the non-linear case in Caputo sense. Finally, some illustrated examples and special cases are also given and considered to show our new approach.

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Keywords

• Caputo fractional derivative
• Riemann-Liouville integral
• matrix Mittag-Leffler functions
• matrix fractional differential equations

MSC

•  26A33
•  32A05

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