Analytic Approach for Solving System of Fractional Differential Equations
Abstract
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.
Keywords
Full Text:
PDFReferences
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.
DOI: http://dx.doi.org/10.23851/mjs.v32i1.929
Refbacks
- There are currently no refbacks.
Copyright (c) 2021 Al-Mustansiriyah Journal of Science

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
ISSN: 1814-635X (Print), ISSN: 2521-3520 (online)