Utilizing the Fractional Reduced Differential Transform Method for Solving Fractional Differential-Algebraic Equations

Authors

  • Haider A. Mkharrib University of Thi-Qar
  • Mohammed Hussein

DOI:

https://doi.org/10.32792/jeps.v15i1.616

Keywords:

Keywords: fractional reduce differential transform Method , Homotopy Analysis Method

Abstract

   In this paper, we  applications of fractional reduce differential transform Method to solving differential-algebraic equations . this method has been tested on some examples and comparisons are made between fractional reduce differential transform Method, Homotopy Analysis Method (HAM).  The results obtained proved that the proposed method is more effective..

References

Chen, W.; Sun, H.; Li, X. Fractional Derivative Modeling in Mechanics and Engineering ; Springer:

Beijing, China, 2022. doi.org/10.1155/2013/279681.

Atangana, A.; Secer, A. A note on fractional order derivatives and table of fractional derivatives of

some special functions. Abstr. Appl. Anal. 2013, 2013, 279681. doi.org/10.1155/2013/279681.

Iskenderoglu, G.; Kaya, D. Symmetry analysis of initial and boundary value problems for fractional

differential equations in Caputo sense. Chaos Solitons Fractals 2020, 134, 109684.

doi.org/10.1016/j.chaos.2020.109684.

Abuasad, S.; Yildirim, A.; Hashim, I.; Karim, A.; Ariffin, S.; Gómez-Aguilar, J. Fractional multi-step

differential transformed method for approximating a fractional stochastic sis epidemic model with

imperfect vaccination. Int. J. Environ. Res. Public Health 2019, 16, 973.

doi.org/10.3390/ijerph16060973

Abuasad, S.; Moaddy, K.; Hashim, I. Analytical treatment of two-dimensional fractional helmholtz

equations. J. King Saud Univ. Sci. 2018, 31, 659–666.doi.org/10.1016/j.jksus.2018.02.002

Saravanan, A.; Magesh, N. An efficient computational technique for solving the Fokker–Planck

equation with space and time fractional derivatives. J. King Saud Univ. Sci. 2016, 28, 160–166.

doi.org/10.1016/j.jksus.2015.01.003

Podlubny, I. Fractional Differential Equations, Mathematics in Science and Engineering; Academic

Press: San Diego, CA, USA, 1999; Volume 198.

Miller, K.S.; Ross, B. An Introduction to the Fractional Calculus and Fractional Differential

Equations; John Wiley & Sons, Inc.: New York,NY, USA, 1993.

Oldham, K.; Spanier, J. The Fractional Calculus Theory and Applications of Differentiation and

Integration to Arbitrary Order; Academic Press: New York, NY, USA, 1974; Volume 111.

Samko, S.G.; Kilbas, A.A.; Marichev, O.I. Fractional Integrals and Derivatives: Theory and

Applications; Gordon and Breach Science Publishers: Yverdon, Switzerland, 1993.

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Published

2025-03-01