Analytic Approach for Solving System of Fractional Differential Equations
DOI:
https://doi.org/10.23851/mjs.v32i1.929Keywords:
Caputo derivatives, Sumudu transform, Mittage-Leffler function and asymptotically stableAbstract
In this paper, Sumudu transformation (ST) of Caputo fractional derivative formulae are derived for linear fractional differential systems. This formula is applied with Mittage-Leffler function for certain homogenous and nonhomogenous fractional differential systems with nonzero initial conditions. Stability is discussed by means of the system's distinctive equation.
Downloads
References
Kılıçman, A., & Altun, O. (2014). Some remarks on the fractional Sumudu transform and applications. Appl. Math, 8(6), pp. 1-8.
Bulut, H., Baskonus, H. M., & Belgacem, F. B. M. (2013, January). The analytical solution of some fractional ordinary differential equations by the Sumudu transform method. In Abstract and Applied Analysis ,Vol. (2013).
Sheikhani, A. H. R., & Mashoof, M. (2017). A Collocation Method for Solving Fractional Order Linear System. Journal of the Indonesian Mathematical Society, 23(1), pp. 27-42.
Ertürk, V. S., & Momani, S. (2008). Solving systems of fractional differential equations using differential transform method. Journal of Computational and Applied Mathematics, 215(1), pp. 142-151.
Li, X., Liu, S., & Jiang, W. (2018). q-Mittag-Leffler stability and Lyapunov direct method for differential systems with q-fractional order. Advances in Difference Equations, 2018(1), pp. 1-9.
Skhail, E. S. E. A. (2018). Some Qualitative Properties of Fractional Order Differential Systems (Doctoral dissertation, Faculty of Science Department of Mathematics Some Qualitative Properties of Fractional Order Differential Systems Submitted by: Esmail Syaid Esmail Abu Skhail Supervisor Dr. Mohammed M. Matar Department of Mathematics, Faculty of Science, Al-Azhar University-Gaza).
Takaci, D., Takaci, A., & Takaci, A. (2017). Solving fractional differential equations by using Sumudu transform and Mikusinski calculus. J. Inequal. Spec. Funct, 8(1), pp. 84-93.
Al-Shammari, A. G. N., Abd AL-Hussein, W. R., & AL-Safi, M. G. (2018). A new approximate solution for the Telegraph equation of space-fractional order derivative by using Sumudu method. Iraqi Journal of Science, 59(3A), pp. 1301-1311.
Bodkhe, D. S., & Panchal, S. K. (2016). On Sumudu transform of fractional derivatives and its applications to fractional differential equations. Asian Journal of Mathematics and Computer Research, 11(1), pp. 69-77.
Belgacem, F. B. M., Karaballi, A. A., & Kalla, S. L. (2003). Analytical investigations of the Sumudu transform and applications to integral production equations. Mathematical problems in Engineering, 2003.
Li, H., Cheng, J., Li, H. B., & Zhong, S. M. (2019). Stability analysis of a fractional-order linear system described by the Caputo-Fabrizio derivative. Mathematics, 7(2), pp. 1-9.
Chaid, A. R. K. K. M. (2016). Stability of Linear Multiple Different Order Caputo Fractional System. Control Theory and Informatics, 6(3), p.55-68.
Downloads
Key Dates
Published
Issue
Section
License
(Starting May 5, 2024) Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution (CC-BY) 4.0 License that allows others to share the work with an acknowledgement of the work’s authorship and initial publication in this journal.
How to Cite
