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Restricted fractional differential transform for solving irrational order fractional differential equations

Author

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  • Khudair, Ayad R.
  • Haddad, S.A.M.
  • khalaf, Sanaa L.

Abstract

Arikoglu and Ozkol developed a new semi-analytical numerical technique, fractional differential transform method (FDTM), for solving fractional differential equations (FDEs). FDTM was not achieved for solving irrational order fractional differential equations. Here we develop a new method to be applicable for solving rational or irrational order FDEs. This method is called the restricted fractional differential transform method (RFDTM). In fact, RFDTM is based on the restriction of the classical two dimensional differential transform methods. A useful theorem is provided, and Several FDEs are solved by using RFDTM. Moreover, several illustrative examples are presented to demonstrate the accuracy and effectiveness of the proposed method.

Suggested Citation

  • Khudair, Ayad R. & Haddad, S.A.M. & khalaf, Sanaa L., 2017. "Restricted fractional differential transform for solving irrational order fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 81-85.
    • Handle: RePEc:eee:chsofr:v:101:y:2017:i:c:p:81-85
    DOI: 10.1016/j.chaos.2017.05.026
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    1. Metzler, Ralf & Klafter, Joseph, 2000. "Boundary value problems for fractional diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(1), pages 107-125.
    2. Arikoglu, Aytac & Ozkol, Ibrahim, 2007. "Solution of fractional differential equations by using differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1473-1481.
    3. Lina Song & Weiguo Wang, 2013. "Solution of the Fractional Black-Scholes Option Pricing Model by Finite Difference Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, June.
    4. Ji-Huan He, 2012. "Homotopy Perturbation Method with an Auxiliary Term," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-7, February.
    5. Arikoglu, Aytac & Ozkol, Ibrahim, 2009. "Solution of fractional integro-differential equations by using fractional differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 521-529.
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    Cited by:

    1. Mousavi, Yashar & Alfi, Alireza, 2018. "Fractional calculus-based firefly algorithm applied to parameter estimation of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 202-215.

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