Solving systems of conformable linear differential equations via the conformable exponential matrix

doi:10.1016/j.asej.2021.02.035

Ain Shams Engineering Journal

Volume 12, Issue 4, December 2021, Pages 4075-4080

https://doi.org/10.1016/j.asej.2021.02.035 Get rights and content

Under a Creative Commons license

open access

Abstract

In this research paper, we discuss systems of conformable linear differential equations. The conformable fundamental exponential matrix has been used to express the solution of the homogeneous and nonhomogeneous systems. The method of variation of parameters has been investigated to find the particular solution of the conformable system of nonhomogeneous linear differential equations. Several illustrative examples have been provided at the end of our study to validate all obtained results.

Keywords

Conformable derivative

Conformable integral

Conformable exponential matrix

Conformable system of differential equations

Cited by (0)

Francisco Martínez is a tenured associate professor at the Universidad Politécnica de Cartagena, Spain. He received PhD degree in Physics from Universidad de Murcia in 1992. His research interests include the nonlinear dynamics methods and their applications, fractional calculus, fractional differential equations, multivariate calculus or special functions, and divulgation of mathematicsield of study should be lower-cased.

Inmaculada Martínez-Vidal is a PhD student of the Industrial Technologies program of the Universidad Politécnica de Cartagena, Cartagena, Spain. She is an industrial engineer from the Polytechnic University of Cartagena since 2012. She is doing her doctoral thesis in the field of fractional calculus and its applications to physics and engineering. She works as an engineer in the Spanish public company NAVANTIA, a benchmark in the design and construction of military ships and high-tech civilian ships and collaborates with the Departamento de Matemática Aplicada y Estadística of the Universidad Politécnica de Cartagena in the divulgation of mathematics.

Mohammed K. A. Kaabar received all his undergraduate and graduate degrees in Mathematics from Washington State University (WSU), Pullman, WA, USA. Mohammed has a global diverse experience in teaching and research. He also worked as an adjunct profesor of mathematics at Moreno Valley College, California, USA. He authored two math textbooks, and he is an invited referee for more than 100 Science, Technology, Engineering, and Mathematics (STEM) international conferences all over the world. He served as an editor for the American Mathematical Society (AMS) Graduate Student Blog, and he is an editorial board member for an educational program at California State University. Kaabar is serving as an associate editor for the Bulletin of Electrical Engineering and Informatics, International Journal of Electrical and Computer Engineering, IAES International Journal of Robotics and Automation, International Journal of Power Electronics and Drive Systems, Journal of Education and Learning, and TELKOMNIKA. He is also a member of the expert editorial advisory board for the Big Data and Advanced Wireless Technologies Springer Book Series. His research interests are fractional calculus, applied mathematics, fractal calculus, numerical analysis, applied analysis, STEM education, and data science.

Silvestre Paredes is a tenured associate professor at the Universidad Politécnica de Cartagena, Spain. He received a PhD degree in Mathematics from the Universidad de Valencia in 1995. His research interests include the study of large scale structure of The Universe, Galaxies Distribution, Cosmology and Astronomy, Fractals and Applications and Fractional Calculus.

: Peer review under responsibility of Ain Shams University.