A class of linear non-homogenous higher order matrix fractional differential equations: Analytical solutions and new technique-Reference-Cited by-同舟云学术

A class of linear non-homogenous higher order matrix fractional differential equations: Analytical solutions and new technique

Published:2020-04-01 Issue:2 Volume:23 Page:356-377
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

El-Ajou Ahmad¹²,Oqielat Moa’ath N.¹,Al-Zhour Zeyad³,Momani Shaher⁴⁵

Affiliation:

1. Department of Mathematics , Faculty of Science Al Balqa Applied University , Salt , 19117 , Jordan

2. Department of Mathematics , Faculty of Science Taibah University , Madina , Saudi Arabia

3. Department of Basic Sciences and Humanities , College of Engineering Imam Abdulrahman Bin Faisal University , P. O. Box 1982 , Dammam , 31441 , Saudi Arabia

4. Department of Mathematics , Faculty of Science University of Jordan , Amman , 11942 , Jordan

5. Department of Mathematics and Sciences College of Humanities and Sciences , Ajman University Ajman , Ajman , United Arab Emirates

Abstract

Abstract In this paper, our formulation generalizes the fractional power series to the matrix form and a new version of the matrix fractional Taylor’s series is also considered in terms of Caputo’s fractional derivative. Moreover, several significant results have been realignment to these generalizations. Finally, to demonstrate the capability and efficiency of our theoretical results, we present the solutions of three linear non-homogenous higher order (m − 1 < α ≤ m, m ∈ N) matrix fractional differential equations by using our new approach.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2020-0017/pdf

Reference35 articles.

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3. Z. Al-Zhour, The general (vector) solutions of such linear (coupled) matrix fractional differential equations by using Kronecker structures. Appl. Math. Comput. 232 (2014), 498–510.

4. Z. Al-Zhour, New techniques for solving some matrix and matrix differential equations. Ain Shams Eng. J. 6 (2015), 347–354.

5. S. Barnett, Introduction to Mathematical Control Theory. Oxford University Press, Oxford (1975).

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