Analytic Approach for Solving System of Fractional Differential Equations

Nabaa N Hasan; Zainab John

doi:10.23851/mjs.v32i1.929

Analytic Approach for Solving System of Fractional Differential Equations

Nabaa N Hasan, Zainab John

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

Caputo derivatives, Sumudu transform, Mittage-Leffler function and asymptotically stable

Full Text:

PDF

References

Kılıçman, A., & Altun, O. (2014). Some remarks on the fractional Sumudu transform and applications. Appl. Math, 8(6), pp. 1-8.

CrossRef

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).

CrossRef

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.‏

CrossRef

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.‏

CrossRef

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.

CrossRef

‏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.‏

CrossRef

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.

CrossRef

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.‏

CrossRef

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